Limits & Continuity Questions and Answers

Consider the function f x following Simplify your answer x f x x 3 x 2 2x 1 x 2 and use exact values Compute each of the

Consider the function f x 1 2x 4 x 1 The absolute maximum value is and this occurs at x The absolute minimum value is and this occurs at x

The graph below is the function f x 5 4 3 2 1 5 4 3 N 2 1 1 3 4 1 2 3 4 5 Select all statements below that you agree with Note You may be checking more than one box No partial credit f 2 is defined lim x 2 f x exists f x f 2 lim x 2 The function is continuous at x 2 O The function is not continuous at x 2

Simplify the expression and eliminate any negative exponent s Assume that all letters denote positive numbers a w8 7w6 7 w1 7 b a7 4 2a3 4 3

Let F x f x6 and G x f x 6 You also know that 5 a 14 a 3 a 13 a 5 Then F a and G a

Evaluate the limit 6x 11 lim XX 8x 11x 10

Convert each degree measure to radian measure as a multiple of Do not use a calculator a 30 b 10 radians

Evaluate the limit or show it does not exist explain your work if you evaluate Make the a lim Suize limit 2xy x y 12 y 2x 6 lim to x y 0 0 2xy y 2x

Put each fractional expression into standard form by rationalizing the denominator a 5 3 b 2 c 31 0

Evaluate each expression a 323 S b 64 1 2 81 3 4 16

20 Sketch a graph of each equation Label all key point a 4x 9y 36 b 3y 4x 12

Let f be a differentiable function of z If y f x define the differential of y dy at r

Let f be a function of a single variable r Write the formal definition of the derivative at a Fill in each blank with the correct derivative

means Let f be a function of z Write the formal definition for what it means for f to be continuous at a c Let f be a function of a single variable r Write the formal definition of the derivative at z

Guess the value of the limit if it exists by evaluating the function at the given numbers It is suggested that you report answers accurate to at least six decimal places tan 3x tan 5x 2x Let f z We want to find the limit lim z O tan 3z tan 52 21 x Start by calculating the values of the function for the inputs listed in this table f T 04 0 2 0 1 0 05 0 01 0 001 28 7 0 0001 38 5 Based on the values in this table it appears lim Z O Xo 0 0 of 0 X OF tan 32 tan 5x 2x z3

Evaluate the following limits If needed enter oo for 00 and oo for 00 371 11 6x a lim I H b lim I H 37T 11 6x

If 6 and y 1 25 find y 1 by implicit differentiation

Evaluate the limit 1 8z lim I 10 11z

Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0 01 cm thick to a hemispherical dome with a diameter of 65 meters cubic centimeters

sin na Hint Consider the Fouries series of the function which is equal to 1 for r a and 0 for other re

e table shows the time a patient spends at the entist and the amount of the bill Bill Amount for Time Spent at the Dentist Time spent at the Bill dentist in hours amount 14 235 867 156 215 27 0 75 1 6 What is the correlation coefficient for the data in t table O 0 93 O 0 27 0 27 0 93

Consider the surface F x y z x6z8 sin y z 10 0 Find the following partial derivatives dx

1 point If z sin V dz du dz am 11 and x In u and y find the following partial derivatives using the chain rule Enter your answers as functions of u and

For the function f x 5x 4x evaluate and fully simplify each of the following f x h f x h f x h 11

Express the function h x Your answer is f x 1 in the form fog If g x x 3 find the function f x x 3

A certain group of test subjects had pulse rates with a mean of 82 1 beats per minute and a standard deviation of 125 beats per minute Would it be unusual for one of the test subjects to have a pulse rate of 156 9 beats per minute Minimum usual value beats per minute Type an integer or a decimal CITS

Find the exact value of sin I in simplest form I 9 V58 K 23 J

Question 12 Listen The profits for a company can be modeled by the logarithmic function P t log 2t 1 With P in thousands of dollars and t in years What is instantaneous increase in profit at year 3 a 5373 46 dollars year b 0 19 dollars year c 186 10 dollars year d 5 37 dollars year Question 13 1 point 40 Listen How much more intense is an earthquake of magnitudo Saved

E 8 points Given r t t cos 2t sin 2t find the unit tangent and unit normal vectors T and N Then show that I and N are orthogonal

1 point Find the limits if they exist or type DNE for any which do not exist 1 Along the x axis 2 Along the y axis 3 Along the line y mx 4 The limit is 3x lim x y 0 0 4x 4y

Show that 2t e H t e H t e t e t H t

1 point For the curve given by r t 5 sin t 2t 5 cos t Find the unit tangent T t Find the unit normal N t Find the curvature k t 2

The position function of a particle is given by r t 5t 5t t 4t At what time is the speed minimum

Find the unit tangent vector at the indicated point of the vector function T 2 r t et costi et sintj et k

1 point Consider the line with these parametric equations x 6t 9 y 4t 7 z 4t 2 One set of symmetric equations for this line is where yo where y Zo Another set of symmetric equations for this line is b Z1 b x 9 y Yo 6 b and c X y 3 Z ZO 2 21 b and c zo C C Z1

Which equation is equivalent to log 36 27 O 2 36 0x x 36 36 2 2 262

What is the value of log 43 Use the calculator Round your answer to the nearest tenth 0 6 1 6 3 8 4 7

1 point Find a b if a 5 b 8 and the angle between a and b is a b radians

What are the domain and range of f x logx 5 O domain x 0 range all real numbers Odomain x 0 range all real numbers domain x 5 range y 5 Odomain x 5 range y 5

Find a and 3 that solve the vector equation Suppose the above equation is expressed as Ax b with 8 Express the coeffieints of the equations in on matrix form as Ab X b 1 17 B 7 3 31 Complete the missing column of the following matrix derived by doing row operation of the augmented matrix in a c 1 2 0 1 d B

Textbook Videos Use part I of the Fundamental Theorem of Calculus to find the derivative of Xx f x 1 t 1 4 dt

Textbo Use Part I of the Fundamental Theorem of Calculus to find X 3 Videos each of the following when f x f x t dt

Textbook If f x 1 0 x x 3 t dt then Videos Videos

When estimating distances from a table of velocity data it is not necessary that the time intervals are equally spaced After a space ship is launched the following velocity data is obtained Use these data to estimate the height above the Earth s surface at 127 seconds t sec 0 6 17 23 45 60 67 127 v ft s 0 132 374 506 990 1320 1649 4469 lower estimate of distance traveled 26 11 omiles upper estimate of distance traveled miles

Use geometry not Riemann sums to evaluate the following definite integral Sketch a graph of the integrand show the region in question and interpret your results 5 f x dx where f x 0 OA 6 if x 4 3x 6 if x 4 Sketch a graph of the integrand and then shade the region in question Choose the correct graph below 5 ff x dx X o 2 B Z Simplify your answer Type an integer or a decimal Q Q Q F

Use summation properties and formulas to rewrite and evaluate the sum 24 5k 1k 6 k 1

3 Find the value of the summation 4 k k 2 k 0 C

Next question can retry this question below Get a similar question n 6 1 4 4 6 i cos i n i 1 express the limit as n provide a b and f x in the expression Given Rn as a definite integral that is f x dx ob You a

15 5 1 A 5 7 5 1 5 9 by the LU decomposition method b 4 14 2

0 Mr Tong s family went to the movies and bought two adult tickets and one child ticket and paid 48 Mr Robert s family went to the movies and bought 5 adult tickets and two child tickets and paid 120 What is the total amount Mr Tong s family paid for adults A 24 B 32 C 48 S D 56 310616668