Calculus Help with Assignment

Calculus (Latin, calculus, a small stone used for counting) is a branch in mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.

(Source: Wikipedia)

Example problems for calculus help with assignment

Calculus help with assignment problem 1:

Differentiate the given function with respect y and find the value of g'(y). The given function is g(y) = 0.45y3 + 3.3t2 - 4y4 + y5

Solution:

The given function is g(y) = 0.45y3 + 3.3t2 - 4y4 + y5

Differentiate the given function with respect to x, we get

g'(y) = (0.45 * 3)y2 + (3.3 * 2)y - (4 * 4)y3 + 4y4

= 4y4 - 16y3 + 1.35y2 - 6.6y

Answer:

The final answer is 4y4 - 16y3 + 1.35y2 - 6.6y

Calculus help with assignment problem 2:

Differentiate the given equation with respect to t, y = 23t5 + 42t3 - 9t2 - 16

Sol:

Given y = 23t5 + 42t3 - 9t2 - 16

Differentiating both sides, we have

`(dy / dt)` = (23 * 5)t4 + (42 * 3)t2 - (9 * 2)t - 0

= 115t4 + 126t2 - 18t

`(dy / dt)` = 115t4 + 126t2 - 18t

Answer:

The final answer is 115t4 + 126t2 - 18t

Calculus help with assignment problem 3:

Integrate the given function ∫ (9x2) dx

Solution:

The given function is 9x2 dx

Integrate the given function with respect to x, we get

∫ (9x2) dx = 9 `(x^3 / 3)` + c

= 3x3 + c.

Answer:

The final answer is 3x3 + c

Calculus help with assignment problem 4:

Integrate the given function g(x) and find the value of G(3). The given function is g(x) = 14x6 - 5x4 + 28x + 40

Solution:

The given function is g(x) = 14x6 - 5x4 + 28x + 40

Integrate the given function with respect to x, we get

G(x) = 14 `(x^7 / 7)` - 5 `(x^5 / 5)` + 28 `(x^2 / 2) ` + 40x + c

= 2x7 - x5 + 14x2 + 40x + c

Find the value of G(3):

Substitute x = 3 in the above equation, we get

G(3) = 2 (3)7 - (3)5 + 14 (3)2 + (40 * 3)

= 4374 - 243 + 126 + 120

= 4377

Answer:

The final answer is 4377

Practice problems for calculus help with assignment

Calculus help with assignment problem 1:

Find the value f'(2). Given function f(x) = 12x3 - 4x2 + 9

Answer:

The final answer is 128

Calculus help with assignment problem 2:

Integrate the given function g(x) = 6x2 + 12. Find the value G(4).

Answer:

The final answer is 176