## Calculus Questions and Answers

### Evaluate the limit of the function [(3+h)^2-9]/h, if h approaches to 0.

### Evaluate the integral of 1/ ( 1 + 4x^2)

### Find the area bounded by y=8-x^2 and y=x^2.

### A curve has dy/dx=3x^2-2x. The curve passes through the point (2;5). What is the equation of the curve?

### What are all the critical points of f(x)=sinx+cosx ? 0=<x=<2pi

### Differentiate xcos2x. derivative of xcos2x is =?

### Find the equation of a curve that passes through the point (1;4) and dy/dx=4x^3+4x

### If y = sin x + cos 3x, find the third derivative of y?

### Using l'Hopital' Rule, find the limit of x^x^2 as x approaches 0 from the right.

### What is the area of the region bounded by the curve y=square root(x-1), y axis and y=1 to y=5 ?

### Prove that limit of the function (a^x-1)/x=lna,x->0,using two methods.

### What is the limit of the fraction tan4x/tan2x, x-->0 ?

### How to integrate cos^7 x*sinx?

### Determine the limit of the function (sin5x-sin3x)/x, x-->0

### y= Arcsin^2x-2x+2√1-x^2 Arcsin X

### Evaluate the anti derivative of e^2x * cos 3x.

### what is the limit of the function (1-sin x)/cos^2 x, x -> 90 degrees?

### What is the definite integral of y=sin2x/square root(1+sin^4 x)? the upper limit of integration is pi/2 and the lower limit is 0

### Calculate area bounded by the curve y=cosx/(sin^2x-4), x axis and the lines x = 0 and x = pi/2 .

### A company wishes to manufacture a box with a volume of 44 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minimumamount of material.

### What is the limit of the function sin x/(1-2sin^2x) -cos x/(2cos^2x-1) - sin2x/cosx, if x approaches to pi/4?

### Evaluate the limit of the function (2x-sin2x)/x^3; x-->0.

### I need to evaluate the limit of function y=(1-cos2x)/x^2, using trigonometric identities. x approaches to 0.

### Determine using calculus dy/dx if y =arcsin x/(1-x^2)?

### Calculate the second order linear derivatives fxy, fyx for the given function f(x,y)=x^3+8xy

### What is the minimum value of 4x^2-8x-18 ?

### What is the area of the region enclosed by the curves y=lnx and y=ln^2x ?

### What is f'(x) if f(x)=x^(sin x)?

### solve the limit of the function f(x)=sin5x/sinx if x --> pi

### Evaluate the integral using the fundamental theorem of calculus.y=4x^t + 5x^-1 + 6sinx.

### What is the extreme value of 2x^3+3x^2-12x+5?

### Evaluate the limit of I(a), if a goes to infinite. I(a) is definite integral of (2x-3)*e^x, ifx=-a to x=0

### How do you find the extreme points of the function f(x) = 0.25x4 + 3x3 – 18x2 + 10 and classify them?

### What is the second derivative of the function f(x)=2x^3+e^2x+sin 2x-lnx?

### Evaluate the indefinite integral of the fraction 1/(16x^2+24x+9)?

### What is f(x) if f'(x)=25x^4+2e^2x ?

### Evaluate the limit of the function ln(1+x)/(sinx+sin3x) x-->0

### Find f(x) if f'(x)=11e^x/(11+e^x).

### Determine the gradient vector of the function f(x,y)=x^3*y^2-2x at the point (2,4)?

### Evaluate the integral `int (x*e^(2x))/(2x+1)^2 dx` .

### Find the limit of the function (x^2+2x-3)/|x-1| if x approaches 1 from the left.

### Definite integral. How to find the value of definite integral of an exponential function, if the base is >1 and the limits of integration are 0 and 1?

### How to determine the indefinite integral of e^square rootx/square rootx (substitution or parts) ?

### What is the integral of y=(e^(13x)+sin x)/10

### Evaluate the limit of the fraction (x^2-4)/(x^2+x-6) as x approaches to 2.

### Evaluate the definite integral: definite integral of y=4x^7+5x^-1+6sinx if x=1 to x=2.

### math Given I = Integral x^n/(x+1) demonstrate that I <= 1/(n+1). The limits of integration are x=0 to x=1 and n is natural number.?????

### Antiderivatives Determine the antiderivative of y=1/(x-1)(x+4).

### Definite integral of x^2/sqrt(x^3+1), between 2 and 3, gives=?

### Find derivative of the fraction (3x^3+3)/(3x^3-3) .

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