Calculus Answers

ACTIVITY IN BASIC CALCULUS

BASIC RULES IN DERIVATIVE

Name: ____________________ Grade & Section: _______________ Date: __________

  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 - "\\xlongequal{x}"

 4. ( )

√

The temperature at a point is given by T = xyz. Find the average temperature in the cube

with opposite corners at (0,0,0) and (2,2,2).

Determine the average value of F(x, y, z) = xyz throughout the cubical region D

bounded by the coordinate planes and the planes x = 2, y − 2, z = 2 in the first octant.

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 - "\\xlongequal{}"

4.f (x) = "\\xlongequal{}" - _____x² + "\\sqrt[4]{x}"

Find the volume of the region bounded above by the plane z = y/2 and below by the

rectangle.

R ∶ 0 ≤ x ≤ 4,0 ≤ y ≤ 2

Find the volume generated if the region enclosed by y = x² and the line y = 2x is revolve about the x-axis. Answer in 2 decimal places.

Find the volume of the solid obtained by rotating the region bounded by y = x^2 +1 and y = 9 – x^2 about y = -1.

A piece of string whose length is 32cm is cut into 2 pieces. one piece is used to form an equilateral triangle and the other to form of the circle so that the sum of the areas is a minimum? Find the minimum sum of the areas. Express your answer in pi. What is the function

Computation of derivative

Computation of Critical numbers

Computation of minimum value

Represent the sum of first terms of the series 3+33+333+.........

using the sigma notation.

Differentiate y= cos (6x +2)