Single Variable Calculus Answers

Introduction to single variable calculus answers:

Single variable calculus answer deals with the problems containing single variable, where the answer term contain single variable only. Generally calculus is mainly used to calculate the rate of change of given function. Calculus was developed by two mathematicians called Gottfried Leibniz and Isaac Newton and they divide the calculus into differential calculus and integral calculus.

Here we are going to discuss about the single variable answers from both the integral calculus and differential calculus. The following are some of the example problems for single variable calculus answers.

Problems on Single Variable Calculus Answers:

Example 1:

Reduce the integral of the given equation 6y2+18y dy

Solution:

∫6y2+18y dy = ∫6y2 dy +∫18y dy

Integrate the above equation

We get

=6y3/3 + 18y2/2

Simplifying the above equation we get

=2y3+ 9y2

Example 2:

Reduce the following expression by integrating

2et + 13et  .

Solution:

The given expression is  2et + 13et

= ∫ 2et+ 13 et dt

= ∫ 2 et dt + ∫ 13 et dt

By integrating the above, we get as follows

= 2et+ 13 et + c

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Problems on Single Variable Calculus Answers:

Example 1:

Calculate the derivative dy / dt where y = arcsin t.

Solution:

arcsin t is the inverse function of sin t and

sin (arcsin(t)) = t

y = arcsin t so that

sin y = t

Differentiating the above equation, with respect to t, using the chain rule on the left side.

dy/dt cos t = 1

Solve for dy/dt;

dy/dt = 1 / cos y

= 1 / cos ( arcsin t)

= 1 / sqrt(1 - sin 2(arcsin t))

= 1 / sqrt (1 - t 2)

Example 2:

Calculate the coefficient y from the given equation

f (y) = y 4 – 108y + 100

Solution:

The given function has the set of real numbers, the first derivative is

f '(y) = 4 y 3 - 108

f '(y) has real numbers. put f '(y) = 0

4 y 3 - 108 = 0

Add 108 on both sides,

4y 3– 108 + 108 = 108

4y 3= 108

y 3 = 27

y = 3 or y = -3

y = 3 or y = -3 is the solution for the given equation.