Calculus Questions

Find the absolute minimum and absolute maximum of f x x 4x 5 on the interval 1 5

A drug taken orally is absorbed into the bloodstream at the rate of te 0 5t milligrams per hour where it is the number of hours since the drug was taken Find the total amount of the drug absorbed in mg during the first 6 hours Round your answers to two decimal places mg absorbed amount absorption rate mg Hours a Solve without using a graphing calculator 6 b Verify your answer to part a using a graphing calculator mg t

Find all the relative extrema and sketch the graph OF F X x 6x 10 3 2

A boat sailing due West toward a point y 150 feet directly North of you makes an angle of 48 as shown in the diagram y 48 Find the distance in ft between you and the boat Round your answer to the nearest integer A

Sketch the graph of the function showing the amplitude and period y 5 cos 2t y 5 0 34 T O st t 2T y s DO 5 y M M 2T O st

Find the integral Hint Separate the integral into two integrals using the fact that the numerator is a sum or difference and find the two integrals by two different formulas Remember to use absolute values where appropriate Use C for the constant of integration 1 x 9 x 0 dx

Find the integral by whatever means are necessary either substitution or tables Remember to use absolute values where appropriate Use C for the constant of integration 1 25 X dx X

Solve the differential equation and initial condition and verify that your answer satisfies both the differential equation and the initial condition y v y 6x5 Ly 0 1

Sketch the parabola and line on the same graph y 3x 5 and y 2x 3 O V No Solution Help 3 2 25 24 23 22 21 20 19 18 17 16 15 14 13 12 14 10 9 8 7 6 S5 NE 4 3 2 1 42445 2 Find the area between them from x 0 to x 3 square units 2 Fill WebAssign Graphing Tool Graph La After you can use propertie

Use integration by parts to find the integral Hint Take u x dv xex and use a substitution to find v from dv Use C for th constant of integration x ex dx

A factory is discharging pollution into a lake at the rate of r t tons per year given below where t is the number of years that the factory has been in operation Find the total amount of pollution discharged during the first 7 years of operation Round your answer to two decimal places r t t 1 tons

Find the area between the curve y x 2 and the line y 2x 3 shown below from x 0 to x 3 y 11 9 7 5 53 3 square units 2 y x 2 y 2x 3 3

Find the general solution of the differential equation or state that the differential equation is not separable Enter NOT SEPARABLE if the equation is not separable y y 8x

Find the indefinite integral Use C for the constant of integration Remember to use absolute values where appropriate e av x dx X

Find the indefinite integral Use C for the constant of integration Remember to use absolute values where appropriate 45x 45x2 3x1 30e x dx

Find the derivative of the function f x f x 4x 6x In x 1

December 15 2023 1 Integrate the following expressions a S 5x x 12 dx b S 5x 4x dx odnalgus oils gaivlover vd basera x 2x 2 A ball is rolling down a slope with an acceleration noget up J21 up J2ift ori sins veri 01 10802 Tir 1080251 3w elxs t a 4 2t where t is the time in s Find the bal f time if v 5 m s when t 0 babnued noigeted to abiono s ruod

F x x 3x 2x 8x 4 X4 3 Find first second third derivative

F X 3 X4 X Find second derivative

F x x 3x 2x 8x 4 Find first second third derivative

Find the derivative of G X 3x 4x 5 using Chain ful

7 6 points Use the following information to produce a graph of the function f over the closed interval 2 5 The graph of f is continuous The graph starts at the point 2 3 The derivative of f is the function graphed here 1 2 2 1 1 1 3 2 1 1 2 Graph of f x 1 2 Graph of f x 3 3 4 4 5 5

1 Determine the average rate of change of y in the function y x 7x 10x 16 over the interval 1 5 5 marks 2 The distance travelled by an object is modelled by the function d t 6t 60t 151 where di conferents the distance natres and converents the time in raconde Estimata

1 ola 19 If f a Jo VB 2dt dt which of the following is FALSE HINT The integrand is positive when defined OFONTE DEL SI elsy Dini odt buidat B f is continuous at x for all x 0 E f 1 0 A f 0 0 1 C f 1 0 D f 1 3

Express the given quantity as a function f x of one variable x The product of two numbers x and y whose sum is 24 Hul

The graph of y f x is shown to the right Identify the x coordinates of the points where f x has a local minimum N a b e fg h o Which of the following shows every x coordinate where f x has a local minimum Choose the correct answer below OA b e g OB c f D c f h OC a c f

Use Laplace transforms to solve the following differential equations 4 y 5y 4y et sinht with y 0 1 y 0 0 Show the full explanation for this problem

Use a calculator to complete the following table to five decimal places n 10 100 1 000 10 000 100 000 1 000 000 10 000 000 00 1 er 2 59374 e 2 718281828459 CH Complete the following table Round to five decimal places as needed n 10 100 1 000 10 000 100 000 1 000 000 10 000 000 1 in n 2 59374

Aboat is being pulled toward a dock as shown in the figure to the right If the rope is being pulled in at the rate of 4 feet per second how fast is the distance between the dock and the boat decreasing when it is 3 feet from the dock CO Boat Rope The distance between the dock and the boat is decreasing by feet per second when the boat is 3 feet from the dock Round to the nearest thousandth as needed 3 ft Dock

12 2x 3 c 2 2 2

2x 3 c 2x 2

2x 3 c 2x 2 2

4 THE SUBSTITUTION RULE If u g x is a differentiable function whose range is an interval I and f is continuous on I then f f g x g x dx f f u du EXAMPLE I Find x cos x 2 dx u x 2 so du 4x dx x dx du 4 x cos x 2 dx cos u du cos u du sin u C sin x4 2 C 8 x x 5 dx 10 3 2 4 dt C

ban saat 8 00 de evin den kan Serdar ret men g rev yapt dersa neye ayn y nde y r yerek gitmi tir 5 3 v m s H z zaman grafi i ekilde o ki gibi olan Serdar ret menin evi ile dersane aras uzakl k ka m dir 120 200 t

s x 3e2ln x 3 22 1 4

1 2 I zx x n

6 r x sin x cos x 2 0 7

q x x 4x 5 2 3

Consider the function f x derivatives are given by f x 16x x 4 x 4 x 4 The first and second 16 4 3x x 4 14 Find the horizontal asymptotes A y 2 B y 1 C y 0 D DNE 15 Find the intervals where the function is increasing A 2 3 2 3 B 0 2 3 C 0 D 0 0 16 Find the inflection points Lo LOG ENT 910 A 2 3 0 5 B 0 1 C 2 3 0 5 2 3 0 5 E DNE

In ln x lima In 2

cos x lima x n r

limx In x 1 In x

limx 0 32 22 x

2x 1 limx 3 1

3 n n is an n th Riemann sum on the interval 0 1 so AX Rn n lim Rn n x n n HINT The limit is a definite integral from 0 to 1 You just have to figure out the function being integrated A 1 R 1 2 C 3 2 D 2 3 E 2

13 An apple orchard now has 30 trees per acre and the average yield is 400 apples per tree so the crop is 12 000 apples per acre For each additional tree planted per acre the average yield per tree is reduced by 10 apples How many trees per acre will give the largest crop of apples HINT Let X be the number of additional trees per acre Then there are 30 X trees per acre and the yield per tree is 400 10X This is enough to determine the crop per acre which is what you want to maximize 007 3 LOST A 30 B 35 C 40 D 45 atute 2 2122 pouth seanq 734 Shton 30th ya

20 Which of the following statements about indefinite integrals are true I f f x g x dx f f x dx f g x dx II f f x g x dx f f x dx f g x dr III ff g x g x dx f g x C f x 1 IV f f x dx n 1 C A only I and II are true B only I and III are true C only E only I I and IV are true D only I II and IV are true III and IV are true

11 A plane flying horizontally at an altitude of 9 mi and a speed of 470 mi h passes directly over a radar station Find the rate at which the distance from the plane to the station is increasing when it is 10 mi away from the station

14 Find the horizontal asymptotes to Hoid 192 LAS A y 2 amwollol B y 1 C y 0 D DNE

car moves along the x axis with position from the starting point given by some function S t If the acceleration a t S t is positive then the SPEED is A Is increasing B Is decreasing C Can t tell without more information i e may be increasing or decreasing