Calculus Answers

Prove that x(1 + x) > (1 + x) In(1 + x) > x

Write the formula to find massof an object in 2-D coordinate system

Find the asymptotes of y^2(a+x) =x^2(3a-x) parallel to coordinate axes

Find the derivative of the given function.

1.) y = (x ^ 3 - 3)(x ^ 2 + 4x + 1)

2.) y = (7x + 3)(x ^ 4 - x ^ 3 - 9x)

3.) y = x ^ 2 * (2x ^ 2 + x + 1)

4.) y = (x ^ 2 - 10x + 2)(x ^ 3 - 2x ^ 2 + 1)

5.) y=(x^ 2 -2x-1)(x+)

6.) y= sqrt x( x^ 3 -2x^ 2 +7x-1)

7.) t = x ^ (1/3) * (x ^ 2 - 5x + 2)

8.) y = (5x ^ 2 - 13)(x ^ 3 + 6x + 1)

9.) y=x^ -2 (x^ 2 +7

10.) x ^ - 5 * (x ^ 2 + 10x - 5)

7. Differentiate the function x = y ^ 4 - 2y ^ 3

8. Differentiate the function t = 1/2 * t ^ 4 - 5t - 3

9. Differentiate the function y = (x ^ 2 - 2) ^ 2

10. Differentiate the function y = 1/(x + 7)

11. Find the slope of function y = 1/(x ^ 2), 12, 1/4 12. Find the slope of function y^ 2 =4x.(1,2)

13. Find the slope of function y = 1/(x + 1), (- 2, 1)

find the centroid and boundaries y=x^2 and the line y=x

ACTIVITY IN BASIC CALCULUS

BASIC RULES IN DERIVATIVE

 Complete the blanks of the given function below with a number (except 0 and 1) to create your own problem and find the derivative of the function. Show your complete solution to each problem.

1. f(x) = -₄x⁵+ ______x^-4 - 2468

2. f (x) =____x^-3- _____x1/4 - 12x

3.f(x)= ____ "\\sqrt[4]{x^3} - \\underset{x^6}{=} + \\frac{2}{3} x^6"

4.f (x) = "\\underset{x^-6}{=} -"____ x² + "\\sqrt[4]{x}"

The base of the rectangle is changing at the rate of 3in/min. if its height remains constant, determine the rate of change of its perimeter with respect to time?

Suppose 𝑓 is odd and differentiable everywhere. Prove that for every positive

number 𝑏, there exists a number 𝑐 in (−𝑏, 𝑏) such that 𝑓′(𝑐) = 𝑓(𝑏)/𝑏.

The Altitude of a triangle is increasing at a rate of 8cm/s while its area is increasing at the rate of 12cm^2/s. At what rate is the base of the triangle changing when the altitude is 20 cm and the area is 100 cm^2 ?