# Calculus Questions

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Calculus

Application of derivativesGraph 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 CalculusUse 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 equationsFrom 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 CalculusTue 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 CalculusFind 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 derivativesUse 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

Indefinite IntegrationQuestion 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 Integrals4 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 Calculus2 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 derivativesSolve the triangle with the given angles and sides 6 points B 52 C 28 a 43 c

Calculus

Application of derivativesFind 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 derivativesFind the volume of the parallelepiped box determined by u v and w u 4i 2j V 3i j 3k w i 3k

Calculus

DifferentiationFind 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 equationsrms 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 derivatives0 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 derivativesThe 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 derivatives18 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 CalculusA 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 derivativesThe 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 derivativesGiven 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

Application of derivatives5 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 CalculusX Given f x x 3x 2x 1 What is the degree of the function As x approaches negative infinity f x is approaching

Calculus

Vector CalculusFind 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 derivativesFind the solution to the equation given below Exact values only Try again 4x 5 x 0 4024

Calculus

Vector CalculusUse a graphing utility to approximate the real solutions Round to two decimal places x 3x 6x 1 0 Solution 1 Solution 2

Calculus

Vector CalculusSolve the equation 3x 1 10 Show your work Round to one decimal place as needed Solution 1 Solution 2

Calculus

Definite IntegralsThe 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

Vector CalculusUse the properties of logarithms to condense the expression Assume z 6 5 In z In z 5 2 In z 6

Calculus

Vector CalculusA 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 derivativesIf 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 derivativesThe 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 derivativesFind the area of the largest rectangle that can be inscribed in the ellipse 2 y 1 a 62

Calculus

Application of derivativesFind 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 derivativesA 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 derivatives11 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 IntegralsFind 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 IntegralsSketch 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 IntegralsEvaluate 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 IntegralsY 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 IntegralsSketch 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 IntegralsFind 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