Calculus Answers

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- _____x^1/4 - 12x

3.f(x)= ____ "\\sqrt[4]{x^3} - \\underset{x^-6}{=} + \\frac{2}{3}" x⁶

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

Given that the sum of the first four term of an AP is 32, while the sum of the three next terms is 52. Calculate the sum of the first 10 terms of the sequence.

Find the output needed to maximize profit given that the total cost and total revenue functions are TC=2Q and TR=100 ln (Q+1) respectively. 

Find the limit of the following functions using the tabular method.

1. lim    x2+x-6x+3/ x+3

𝑥→−3

1. lim x2-2x+3/ x+1   

𝑥→−1

What positive number added to its reciprocal gives the minimum sum?

5. Express as a double integral the area enclosed by one loop of the curve 𝑟 = 3 cos 2𝜃 and

evaluate the integral

A curve has an x-intercept at * = 1. At its y-intercept of y = -3, the curve's tangent line

has a slope of -1. Find the equation of this curve in the form y

= ax2 + hx+c