# Calculus Questions

The best high school and college tutors are just a click away, 24×7! Pick a subject, ask a question, and get a detailed, handwritten solution personalized for you in minutes. We cover Math, Physics, Chemistry & Biology. Calculus
Application of derivatives
Graph the function not by plotting points but by starting from the graph of y e in the figure below 10 range O 10 O y 10 10 y 10 10 y 2 10 10 X 10 O 10 State the domain and range Enter your answers using interval notation domain y 10 10 10 10 Calculus
Vector Calculus
Use a calculator to evaluate the function at the indicated values Round your answers to three dec h x e h 1 h h 5 h 5 h 1 h h 5 h 5 W Calculus
Differential equations
From the graph determine the x and y intercepts and the vertical and horizontal asymptotes If an answer does not exist ONE Enter your asymptotes as a comma separated list of equations if necessary x intercept y intercept vertical asymptote horizontal asymptote 10 5 y 10 S 5 S 10 M Calculus
Vector Calculus
Tue or False 12 x Let x x 1 2x 4 a The graph of r has a vertical asymptote x 1 O True O False b The graph of r has a vertical asymptote x 2 O True O False c The graph of r has a horizontal asymptote y 1 O True O False d The graph of r has a horizontal asymptote y O True O False Calculus
Vector Calculus
Find all horizontal and vertical asymptotes if any If an answer does not exist enter DNE Enter your answers as a comma separated list of equations r x 3 X 9 vertical asymptote s horizontal asymptote 10 Calculus
Application of derivatives
Use transformations of the graph of y 1 x to graph the rational function as in Example 2 domain 10 range 10 5 5 10 X 10 X 10 State the domain and range Enter your answers using interval notation 10 5 5 2 Calculus
Application of derivatives
150 180 210 120 240 90 270 60 30 2 3 4 300 330 0 Calculus
Indefinite Integration
Question 5 20 points 5 Find the moment of inertia in terms of its mass of a right circular cone of radius r and height h with respect to its axis h Axis Calculus
Definite Integrals
4 Find the radius of gyration with respect to its axis of the solid generated by revolving the first quadrant region under the curve y 4 x about the y axis Calculus
Vector Calculus
2 Refer to the given vectors for the problems that follow 5 points each a Find v 3u u i 2j v i Calculus
Application of derivatives
Solve the triangle with the given angles and sides 6 points B 52 C 28 a 43 c Calculus
Application of derivatives
Find the area of the parallelogram whose vertices are given below A 1 4 B 4 0 C 11 3 and D 6 7 Calculus
Application of derivatives
Find the volume of the parallelepiped box determined by u v and w u 4i 2j V 3i j 3k w i 3k Calculus
Differentiation
Find the area of the triangle determined by the points P Q R P 1 1 2 Q 2 0 1 R 0 2 1 Calculus
Differential equations
rms of Linear Equations Show all calculations in the space provided Please remember to indicate the formula s you use Describe the equations below List and identify the information provided by the equations 1 y 8 x 3 2 y x 3 Place the equation in slope intercept form 3 3x 2y 18 0 3 y 4x 4 y 2 x 5 Calculus
Application of derivatives
0 Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of 0 where 2 3 3 81 9x x 3 cos 0 0 1 1 Then find sin 0 and Calculus
Application of derivatives
The price of a home is 180 000 The mortgage on the hous a 30 year fixed rate mortgage at 4 Use this information to fin the amount of the monthly payment Round your answer to the nearest cent Use the formula below to solve the problem P 1 1 xt PMT 859 35 954 83 012 54 Calculus
Application of derivatives
18 Estimate to the hundredth the area from 1 to 5 under the graph of f f x approximating rectangles and right endpoints 2 x using four Calculus
Vector Calculus
A tree casts a shadow 6 feet long At the same time a person who is 4 feet tall casts a shadow that is 2 feet long How tall is the tree 19 feet 17 feet 15 feet 12 feet Calculus
Application of derivatives
The population of a colony of mosquitoes obeys the law of uninhibited growth If there are 1000 mosquitoes initially and there are 1200 after 1 day what is a The growth rate Round to three decimal places b The population of mosquitoes after 6 days Round to the nearest whole number c When will the population double Round to the nearest whole number Calculus
Application of derivatives
Given that 2 is a zero find the remaining real zeros Show work WILL be required on the exam No approximate answers will be accepted 3 x 4x 3x 2 Solution 1 Solution 2 Calculus
Differentiation
VE vo X Simplify into a single log 2 log x log 4y Calculus
Application of derivatives
5 10 5 5 5 10 For which values in the domain is this graph increasing Give your answer in interval notation Assume the graph extends to finity in both directions Submit Calculus
Vector Calculus
X Given f x x 3x 2x 1 What is the degree of the function As x approaches negative infinity f x is approaching Calculus
Differentiation
X Given that f x 3x 4 and g x x 1 find g f x 76 El Calculus
Vector Calculus
Find where x 2x 0 Write your answer in interval notation Round to one decimal place as needed Try again Left Interval 0 00 Right Interval undefined Edit my response Calculus
Application of derivatives
Find the solution to the equation given below Exact values only Try again 4x 5 x 0 4024 Calculus
Application of derivatives
What is the conjugate of b if a 3 4i and b 2 3i Calculus
Application of derivatives
Question What is a b if a 3 4i and b 2 3i Calculus
Vector Calculus
Use a graphing utility to approximate the real solutions Round to two decimal places x 3x 6x 1 0 Solution 1 Solution 2 Calculus
Vector Calculus
www Find the solution to the equation given below Exact values only e 5 Calculus
Vector Calculus
Solve the equation 3x 1 10 Show your work Round to one decimal place as needed Solution 1 Solution 2 Calculus
Definite Integrals
The graph of f is shown below Evaluate each integral by interpreting it in terms of areas 1 f x dx 1 5 2 f 2 dun 0 3 f x dx Note You can click on the graph to enlarge the image Calculus
Application of derivatives
X Given the two points A 2 3 and B 3 9 Find the mid point Calculus
Vector Calculus
Use the properties of logarithms to condense the expression Assume z 6 5 In z In z 5 2 In z 6 Calculus
Vector Calculus
A fence 8 ft tall runs parallel to a tall building at a distance of 4 ft from the building What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building Round your answer to two decimal places Enter an integer or decimal number more Question Help Message instructor Calculus
Application of derivatives
If C x 14000 400x1 6x 0 0042 is the cost function and p x 1600 7x is the demand function find the production level that will maximize profit Hint If the profit is maximized then the marginal revenue equals the marginal cost units Calculus
Application of derivatives
The frame for a kite is to be made from six pieces of wood The four exterior pieces have been cut with the lengths indicated in the figure To maximize the area of the kite how long should the diagonal pieces be horizontal vertical Queeri a b A Calculus
Application of derivatives
Find the area of the largest rectangle that can be inscribed in the ellipse 2 y 1 a 62 Calculus
Application of derivatives
Find the dimensions of a rectangle with area 1331 m whose perimeter is as small as possible If both values are the same number enter it into both blanks Calculus
Application of derivatives
A right circular cylinder is inscribed in a cone with height h and base radius r Find the largest possible volume of such a cylinder Question Help Message instructor Calculus
Application of derivatives
15 Given a 3 B 5 and a b 7 determine a b Calculus
Application of derivatives
11 The vertices of quadrilateral ABCD are given as A 0 3 5 B 3 1 17 C 7 3 15 and D 4 1 3 Prove that ABCD is a parallelogram Calculus
Definite Integrals
Find the number b such that the line y b divides the region bounded by the graphs of y 36x and y 9 into two regions wi equal area Round your answer to two decimal places b Calculus
Definite Integrals
Sketch the region enclosed by the given curves Decide whether to integrate with respect to x or y Draw a typical approximating rectangle 2 4 x 4 y x y 4 y 4 4 y 2 2 Find the area of the region 2 X X 2 1 1 1 2 2 2 X X Calculus
Definite Integrals
Evaluate the integral and interpret it as the area of a region 2 1 14 sin x 4 cos 2x dx Sketch the region 1 KIN NTH T KI4 10 2 X a 2 416 412 kter X X Calculus
Definite Integrals
Y NOTES y Sketch the region enclosed by the given curves 2 y G 4 2 4 0 6 ASK YOUR TEACHER y 5 cos 6x y 5 sin 12x x 0 0 05 PRACTICE ANOTHER Find its area 0 10 0 15 0 20 0 05 0 10 0 15 0 20 0 25 0 25 X 0 30 X 12 y st 4 3 2 1 y 6 0 05 0 10 0 15 0 20 0 25 5 4 In 3 X 2 1 0 05 0 10 0 15 X 0 20 0 25 0 30 X Calculus
Definite Integrals
Sketch the region enclosed by the given curves 1 y 16x y X 0 16 10 8 y 10 8 aff 2 Find the area of the region Need Help Read It 10 Watch It 15 8 X X y 10 8 10 6 y 10 2 10 8 15 X X Calculus
Definite Integrals
Find the values of c such that the area of the region bounded by the parabolas y 4x c and y c 4x2 is 288 Enter your answers as a comma separated list C Calculus
Vector Calculus
14 sin A B 7 A 24 25 C