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Maths-

General

Easy

Question

If m is the slope of tangent to the curve $e to the power of y end exponent equals 1 plus x to the power of 2 end exponent$ then

$| m | > 1$
$m > 1$
$m > - 1$
$| m | \leq 1$

The correct answer is: $vertical line m vertical line less or equal than 1$

$table row cell e to the power of y end exponent equals 1 plus x to the power of 2 end exponent rightwards double arrow e to the power of y end exponent fraction numerator d y over denominator d x end fraction equals 2 x rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator 2 x over denominator 1 plus x to the power of 2 end exponent end fraction equals m end cell row cell vertical line m vertical line equals fraction numerator 2 open vertical bar x close vertical bar over denominator 1 plus open vertical bar x to the power of 2 end exponent close vertical bar end fraction rightwards double arrow vertical line m vertical line less or equal than 1 text end text text a end text text s end text text end text 2 vertical line x vertical line less or equal than 1 plus vertical line x vertical line to the power of 2 end exponent end cell end table$

Related Questions to study

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If $stack l i m with x rightwards arrow 0 below 1 plus x to the power of 2 end exponent plus fraction numerator f open parentheses x close parentheses over denominator x end fraction$ is equal to e⁷, then $stack l i m with x greater-than or slanted equal to 0 below fraction numerator f open parentheses x close parentheses over denominator x to the power of 3 end exponent end fraction equals horizontal ellipsis horizontal ellipsis$

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parallel

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A particle when projected in vertical plane moves along smooth surface with initial velocity 20m/s at an angle of 60°, so that its normal reaction on the surface remains zero throughout the motion. Then the slope of the tangent to the surface at height 5 m from the point of projection will be

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physics-General

parallel

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physics-General

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physics-General

parallel

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physics-General

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physics-General

System shown in the figure is released from rest when spring is unstretched. Pulley and spring is massless and friction is absent everywhere. The speed of 5 kg block when 2 kg block leaves the contact with ground is (Take force constant of spring k = 40 N/m and $open g equals 10 m divided by s to the power of 2 end exponent close parentheses$

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physics-General

parallel

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In the figure shown the spring constant is K. The mass of the upper disc is m and that of the lower disc is 3m. The upper block is depressed down from its equilibrium position by a distance $delta$ =5mg/K and released at t=0. Find the velocity of ‘m’ when normal reaction on 3m is mg

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physics-General

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