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Question

$f space left parenthesis x right parenthesis equals t a n to the power of negative 1 end exponent invisible function application x minus x$ is decreasing in

$(- \infty, \infty)$
$(0, \infty)$ only
$(- 1,1)$ only
$(- \infty, 0)$ only

hint Hint:

We are given a function. We have to find the interval for which it is decreasing. We will take the first order derivative to find the answer

The correct answer is: $left parenthesis negative infinity comma infinity right parenthesis$

The given function is f(x) = tan^-1x - x
A function is said to be decreasing when it’s first order derivative is negative
It means f’(x) < 0
We will use this condition to find the answer.
Taking the first order derivative of the given function.
f(x) = tan^-1x - x
$f apostrophe left parenthesis x right parenthesis space equals fraction numerator 1 over denominator 1 plus x squared end fraction minus 1 f apostrophe left parenthesis x right parenthesis space less than space 0 rightwards double arrow fraction numerator 1 over denominator 1 space plus space x squared end fraction minus 1 space less than space 0 space space space space space space space space space space fraction numerator 1 space minus space 1 space minus x squared over denominator 1 space plus space x squared end fraction less than 0 space space space space space... left curly bracket space m a k i n g space t h e space d e n o m i n a t o r space e q u a l right curly bracket space space space space space space space space space space space space space space space space space fraction numerator negative x squared over denominator 1 space plus x squared end fraction less than 0 N o w comma space x squared space i s space t h e space p o s t i v e space q u a n t i t y space f o r space a n y space x element of R. space I t space m e a n s space f o r space a n y space r e a l space v a l u e space o f space x comma space x to the power of 2 space end exponent i s space a l w a y s space p o s i t i v e space space space space space space space space space space S o comma space t h e space t e r m space fraction numerator x squared over denominator 1 space plus space x squared end fraction space w i l l space b e space a l w a y s space p o s i t i v e.$
The negative sign make sures that the function is negative i.e. decreasing.
x can take any value of real number.
And the set of real numbers extends from -∞ to ∞.
So, the interval for which given function is decreasing is (-∞, ∞)

We should know the formulas of differentiation. And, we should know the condition for increasing and decreasing function.

The interval of increase of the function $f space left parenthesis x right parenthesis equals x minus e to the power of x plus t a n invisible function application open parentheses fraction numerator 2 pi over denominator 7 end fraction close parentheses$ is

For such questions, we should know different formulas of differentiation.

The interval of increase of the function $f space left parenthesis x right parenthesis equals x minus e to the power of x plus t a n invisible function application open parentheses fraction numerator 2 pi over denominator 7 end fraction close parentheses$ is

Maths-General

For such questions, we should know different formulas of differentiation.

General

physics-

In experiment of the potentiometer wire $A B$ of length 100 cm has a resistance of 10 $capital omega$ , It is connected in series with a resistance R and a cell of emf 2 volts and of negligible internal resistance. A Source of emf 10mV is balanced against a length of 40 cm of the potentiometer wire. What is the value of the external resistance?

physics-General

General

Maths-

The function $f space left parenthesis x right parenthesis equals t a n to the power of negative 1 end exponent invisible function application x$ is

For such questions, we should check the rules of increasing and decreasing function.

The function $f space left parenthesis x right parenthesis equals t a n to the power of negative 1 end exponent invisible function application x$ is

Maths-General

For such questions, we should check the rules of increasing and decreasing function.

General

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If the function $fraction numerator c o s invisible function application x plus K s i n invisible function application x over denominator 2 c o s invisible function application x plus 3 s i n invisible function application x end fraction$ is decreasing in its domain then $K E$

maths-General

General

Maths-

The function $f space left parenthesis x right parenthesis equals 1 plus 1 over x$ is

We have to see the rules for a increasing and decreasing function.

The function $f space left parenthesis x right parenthesis equals 1 plus 1 over x$ is

Maths-General

We have to see the rules for a increasing and decreasing function.

General

maths-

If $l to the power of 2 end exponent plus m to the power of 2 end exponent equals 1$ then the maximum value of $l plus m$ is

maths-General

General

maths-

The minimum value of the function $f space left parenthesis x right parenthesis equals 3 t a n invisible function application x plus 4 c o t invisible function application x$ where $x element of open parentheses 0 comma fraction numerator pi over denominator 2 end fraction close parentheses$ is

maths-General

General

physics-

In the experiment of potentiometer wire $A B$ is 100 cm long shown in figure When AC=40 cm, no deflection occurs in the galvanometer. What is the value of R ?

physics-General

General

physics-

Consider the potentiometer circuit shown. The potentiometer wire is 600 cm long and having restance 15r At what distance from the point A should the jockey touch the wire to get zero deflection in the galvanometer?

physics-General

General

physics-

Circuit for the measurement of resistance by potentiometer is shown. The galvanometer is first connected at point-A and zero-deflection is observed at length PJ=10 cm. In the second case, it is connected at a point $C$ and zero deflection is observed at a length $30 text end text c m$ from P. Then what is the unknown resistance X?

physics-General

General

physics-

The current taken from the 30 V supply and the current through the 6 $capital omega$ resistor are respectively.

physics-General

General

physics

common base amplifier circuit, calculate the change in base current if that in the collector current is 2 mA and $alpha$ =0.98

physicsGeneral

General

physics

The current gain of a transistor in common base mode is 0.99. To change the emitter current by 5 mA. What will be the necessary change in collector current?

physicsGeneral

General

physics

In a transistor amplifier β=62, $R subscript L$ =5000Ω and internal resistance of the transistor is 500Ω. What will be the ratio of power amplification to voltage amplification?

physicsGeneral

General

physics

In a transistor, a change of 8.0 in the emitter current produces a change of 7.8 mA in the collector current. What change in the base current is necessary to produce the same change in the collector current?

physicsGeneral

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is decreasing in

only only only

We are given a function. We have to find the interval for which it is decreasing. We will take the first order derivative to find the answer

The correct answer is:

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In the experiment of potentiometer wire is 100 cm long shown in figure When AC=40 cm, no deflection occurs in the galvanometer. What is the value of R ?

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Consider the potentiometer circuit shown. The potentiometer wire is 600 cm long and having restance 15r At what distance from the point A should the jockey touch the wire to get zero deflection in the galvanometer?

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The current taken from the 30 V supply and the current through the 6 resistor are respectively.

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The current gain of a transistor in common base mode is 0.99. To change the emitter current by 5 mA. What will be the necessary change in collector current?

The current gain of a transistor in common base mode is 0.99. To change the emitter current by 5 mA. What will be the necessary change in collector current?

In a transistor amplifier β=62,=5000Ω and internal resistance of the transistor is 500Ω. What will be the ratio of power amplification to voltage amplification?

In a transistor amplifier β=62,=5000Ω and internal resistance of the transistor is 500Ω. What will be the ratio of power amplification to voltage amplification?

In a transistor, a change of 8.0 in the emitter current produces a change of 7.8 mA in the collector current. What change in the base current is necessary to produce the same change in the collector current?

In a transistor, a change of 8.0 in the emitter current produces a change of 7.8 mA in the collector current. What change in the base current is necessary to produce the same change in the collector current?

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$f space left parenthesis x right parenthesis equals t a n to the power of negative 1 end exponent invisible function application x minus x$ is decreasing in

$(- \infty, \infty)$
$(0, \infty)$ only
$(- 1,1)$ only
$(- \infty, 0)$ only

The correct answer is: $left parenthesis negative infinity comma infinity right parenthesis$

The interval of increase of the function $f space left parenthesis x right parenthesis equals x minus e to the power of x plus t a n invisible function application open parentheses fraction numerator 2 pi over denominator 7 end fraction close parentheses$ is

The interval of increase of the function $f space left parenthesis x right parenthesis equals x minus e to the power of x plus t a n invisible function application open parentheses fraction numerator 2 pi over denominator 7 end fraction close parentheses$ is

The function $f space left parenthesis x right parenthesis equals t a n to the power of negative 1 end exponent invisible function application x$ is

The function $f space left parenthesis x right parenthesis equals t a n to the power of negative 1 end exponent invisible function application x$ is

If the function $fraction numerator c o s invisible function application x plus K s i n invisible function application x over denominator 2 c o s invisible function application x plus 3 s i n invisible function application x end fraction$ is decreasing in its domain then $K E$

If the function $fraction numerator c o s invisible function application x plus K s i n invisible function application x over denominator 2 c o s invisible function application x plus 3 s i n invisible function application x end fraction$ is decreasing in its domain then $K E$

The function $f space left parenthesis x right parenthesis equals 1 plus 1 over x$ is

The function $f space left parenthesis x right parenthesis equals 1 plus 1 over x$ is

If $l to the power of 2 end exponent plus m to the power of 2 end exponent equals 1$ then the maximum value of $l plus m$ is

If $l to the power of 2 end exponent plus m to the power of 2 end exponent equals 1$ then the maximum value of $l plus m$ is

The minimum value of the function $f space left parenthesis x right parenthesis equals 3 t a n invisible function application x plus 4 c o t invisible function application x$ where $x element of open parentheses 0 comma fraction numerator pi over denominator 2 end fraction close parentheses$ is

The minimum value of the function $f space left parenthesis x right parenthesis equals 3 t a n invisible function application x plus 4 c o t invisible function application x$ where $x element of open parentheses 0 comma fraction numerator pi over denominator 2 end fraction close parentheses$ is

In the experiment of potentiometer wire $A B$ is 100 cm long shown in figure When AC=40 cm, no deflection occurs in the galvanometer. What is the value of R ?

In the experiment of potentiometer wire $A B$ is 100 cm long shown in figure When AC=40 cm, no deflection occurs in the galvanometer. What is the value of R ?

The current taken from the 30 V supply and the current through the 6 $capital omega$ resistor are respectively.

The current taken from the 30 V supply and the current through the 6 $capital omega$ resistor are respectively.

common base amplifier circuit, calculate the change in base current if that in the collector current is 2 mA and $alpha$ =0.98

common base amplifier circuit, calculate the change in base current if that in the collector current is 2 mA and $alpha$ =0.98

In a transistor amplifier β=62, $R subscript L$ =5000Ω and internal resistance of the transistor is 500Ω. What will be the ratio of power amplification to voltage amplification?

In a transistor amplifier β=62, $R subscript L$ =5000Ω and internal resistance of the transistor is 500Ω. What will be the ratio of power amplification to voltage amplification?