If is a real-valued differentiable function satisfying and f(0)=0, then f(1) equals

If f(x) = then:

where represents the integral part function, then:

Which of the following function(s) has/have removable discontinuity at

Consider the function f(x)= where {x} denotes the fractional part function. Which one of the following statements is NOT correct?

Statement-I : If , then

is equal to

is equal to-

Statement The sum of the series 1+(1+2+4)+(4+6+9)+(9+12+16)+…+(361+380+400) is 8000.
Statement - II : , for any natural number n.

If in a frequently distribution, the mean and median are 21 and 22 respectively, then its mode is approximately.

The negation of the statement "If I become a teacher, then I will open a school", is :

The value of the definite integral is

So here we used the concept of integrals and simplified it. We can also solve it manually but it will take lot of time to come to final answer hence we used the minimum and maximum method which makes problem to solve easily. So the answer is non of these.

Suppos ef, f' andf'' are continuous on[0, e] and that then the value of

ther

If is a point on the circle whose centre is on the x-axis and which touches the line x+y=0 at (2,-2), then the greatest value of a is

Equation of the circle of radius is