Limits & Continuity Questions and Answers

Find the unknowns in the graph below X 10 90 14 14 Z X y

Verify that f has an inverse function Then use the function f and the given real number a to find f a Hint See Example 1 If an answer does not exist enter DNE f x x 5 a 3 f 3

Consider the following functions from R to R Select all functions that are linear transformations O T T 43 4 T 4 9 Z T X x y 1 2x y

Use log 4 1 386 and or log 9 2 197 to find log 36 log 36

How tall is a building that casts a 68 ft shadow when the angle of elevation of the sun is 35 The building is ft tall Simplify your answer Type an integer or a decimal Round to the nearest hundredth if needed 35

Convert the angle from radians to degrees 8 59 8 59 radians Tyno O

Write the given expression in an expanded form Assume that variables represent positive numbers x x 9 2 x 9 In In x x 9 Do not simplify

252 250 n 6 0 5 points en I pipe is being carried down a hall ht angled turn into a narrower hal st pipe that can be carried horizont

The Schwimmers cost for cable television is giv is the number of months of service Complete pa a Graph C 80 40x for x 50 Use the graphing tool to graph the equation

The 130 juniors at Smithers High School are taking a class trip Three buses will be taking the students and chaperones to their destination and each bus can hold up to 45 people The first bus will be filled to capacity followed by the second and third buses The function f x describes the total number of people on the first bus where x is the number of minutes spent loading the bus If the first bus is boarded at a rate of 15 people per minute what is the domain of the function D x

2NN to sorpol to tomoquicq Find horizontal asymptote of y y to f x 6 x 2 SX 1 theros ant no SX X 8x 2 x 9 OT ONOMAT

Analyze the polynomial function f x x 0 1x 1 6279x 0 31222 Complete parts a b Graph the function using a graphing utility Use the window 3 3 1 by 2 2 1 Ch A EVA B Ed c Use a graphing utility to approximate the x and y intercepts of the graph The y intercept is 0 31222 Type an integer or decimal rounded to five decimal places as needed

A truck has a minimum speed of 8 mph in high gear When traveling a mph the truck burns diesel fuel at the rate of gal mile 0 0040295 900 T 42 Assuming that the truck can not be driven over 63 mph and that diesel fuel costs 1 69 a gallon find the following a The steady speed that will minimize the cost of the fuel for a 650 mile trip H 1 b The steady speed that will minimize the total cost of a 650 mile trip if the driver is paid 13 an hour c The steady speed that will minimize the total cost of a 450 mile trip if the driver is paid 24 an hour

Analyze the polynomial function f x x 4 2 3 x using parts a Determine the end behavior of the graph of the function

The drawing shows a straight wire carrying a current I Above the wire is a rectangular loop that contains a resistor R If the current lis decreasing in time what is the direction of the induced current through the resistor R left to right or right to left If the induced current goes from left to right through the resistor type the letters LTR in the box below If the current goes from right to left through the resistor type the letters RTL in the box Direction of induced current

O 1 with multiplicity 5 and 3 with multiplicity of 2 O1 with multiplicity 2 and 3 with multiplicity of 5 Onone of these answers Question 5 g x 4x5 5x4 2x 1 which one is true about g x as x gets large goes to infinity O g x goes to infinity as x goes to infinity O g x goes to infinity as x goes to infinity O g x goes to infinity as x goes to infinity

x x 3x 4 Complete the table Round your answers to four decimal places f x 3 9 3 99 3 999 4 001 4 01 Use the result to estimate the limit Use a graphing utility to graph the function to confirm your result R x 4 lim 3x

Evaluate the limit assuming that lim f x 1 and lim 3 g x 3 Use symbolic notation and fractions where needed f x 1 34g x 9 lim

Solve the equation by factoring 3x 4x 1

KE Solve the equation by factoring

Solve the equation by factorin 4x 17x 15 Select the correct choice bel

K Solve the equation usin x 9 6x 5 0

ula ve the equation by the quadratic formula 2 5x 24x 16 0

Tanisha Vizquez owns a wallpaper hanging business Her charge C the number of square feet of wallpaper she hangs a Graph C 15 0 20s for s 200

with Xo O and x 1 what is lim xn n 4 2 4 2 Xn 1 Xn tan xn xn Xn 1 tan Xn tan Xn 1

Solve the equation by factoring 1 10t 24 0

If g 5 0 what point is on the graph of g What is the corresponding x intercept of the graph of g The point 5 0 is on the graph of g Type an ordered pair The corresponding x intercept of the graph of g is Type an integer or a fraction

The total cost of producing x units of a certain commodity is C x thousand dollars where C x x 14x2 195x 128 The average cost function is A x For what values of x is A x increasing For what values is it decreasing O Increasing 0 x 16 decreasing x 16 O Increasing x 16 decreasing 0 x 16 O Increasing 0 x 8 decreasing x 8 Increasing r 8

Part 1 of 3 a Find the locations and values of the relative maxima and relative minima of the function on the standard viewing window Round to 3 decimal p necessary The graph of fhas a relative minimum Part 1 3 Part 2 of 3 of 9 8 at x 5 b Use interval notation to write the intervals over which is increasing or decreasing The graph of fis increasing on the interval 0 0 00 8

dentify the location and value of any relative maxima or minima of the function If there is more than one answer separate them with the and button Part 0 2 Part 1 of 21 O The function has no relative minimum 0 0

1 2 Part 0 2 3 4 57 6 7 Identify the location and value of any relative maxima or minima of the function

Determine whether the function is even odd or neither 2 h x 81 x The function h is an even function O The function h is an odd function O The function h is neither even nor odd X

Write the domain in interval notation f x The domain is x 3 x 4 0 0 0 0 0 0 0 0 OVO

Write the domain in interval notation h x The domain is 2 V5 5x 010 7 0 0 0 0 0 0 8

Determine if the given points are solutions to the equation x 3 y 1 a 9 2 b 3 1 13 c 7 Part 1 of 3 a The point 9 2 Choose one a solution Part 2 of 3 b The point 3 1 Choose one a solution Part 3 of 3 113 X 5

Graph the equation by plotting points y x 9 8 7 6 5 4 3 2 9 84 7 6 5 4 34 2 m t 1 2 3 44 5 6 7 oc 12 3 5 6 7 8 9 x 0 X S

3TT 36 Express radians in degrees A 100 B 108 C 235 D 310

41 Find the distance between points 4 2 and 8 0 A 2 17 B 2 37 C 2 5 D 10

33 Draw a 292 angle in standard position A B C D 292 292 292 292 I

32 Sketch 135 in standard position A B 135 C D 135 135 k 135 I

5TT Find the smallest negative angle coterminal with 3 Use radian measure A 10TT 3 B 4T C 7H D

3 Given a right triangle where side a 8 0 and angle A 42 what does angle B Give the result properly rounded off A 128 B 48 C 138 D 58

16 Given cos 8 1 find 6 A 90 B 270 C 0 D 180

10 Given A C D 8 15 B 15 8 1010000 101000 15 8 co 1004 cose 15 8 17 and is in Quadrant III find tane

5 Given sin 8 1 find csce A 0 B undefined C 1 D 1

Given the following velocity function of an object moving along a line find the position function with the given initial position Then graph both the velocity function and position function v t 3 t s 0 5 312 s t 2t 5 Choose the correct graph below OA Ay 00 X 8 Q G OB O C 8 Q OD Q

Use the limit comparison determine the convergence series below 00 n J n 4 test to of the 1 n 1 n n 2 n 32m

Given the equation below find dy dx y 288x7 600xy 60 10x 2y 59 Now find the equation of the tangent line to the curve at 1 1 Write your answer in mx format 288x7 600x54 60 10x 2u dx x 36x 10x60y y 47 288x 600x y 7 60 10x 2 X

r 0 te tsin 2 71 2t 1 a Find the domain of the vector function r t

Suppose that the continuous function f R Ris periodic that is there is a number p 0 such that f x p f x for all x Show that f R R is uniformly continuous