Limits & Continuity Questions and Answers

4 f x x 5 2 4 3 2 0 54 3 2 1 0 2 3 1 2 3 4 5

3 f x 2x 31 5 4 3 2 1 0 54 3 2 1 d 2 3 1 2 3 4 5

3 Find the length of the hypotenuse X cos a 5 8

s there a midline on this graph the amplitudes are exponential and getting bigger but that wouldn t change the midline don t think would it b C 1 AAA 0 5 ob of ensibar molt 4 an MA 7 1 Periodic Perioa 2 midline 0 AMP None

Given the following table with selected values of f x and g x evaluate f g 1 6 4 1 3 4 f x 4 1 6 1 3 g x 1 4 3 4 6 X 04 0 1 1

Solve for all values of x log5 x 4 log5 x 4 1

Solve for x 1 279936 3x 11 1296 x

Yusuf is going to invest in an account paying an interest rate of 6 5 compounded quarterly How much would Yusuf need to invest to the nearest ten dollars for the value of the account to reach 1 330 in 6 years I

Find the specified nth term in the expansion of the binomial x 8y 5 n 3

14 Determine whether the series given by k 1 a converges to c diverges b d k 1 converges to converges to 4 63 49

15 Determine whether the series given by x 1 2K 32k a b converges diverges

16 Determine whether the series given by a c converges absolutely converges conditionally o 1 k 1 3k b diverges

6 Find the asymptotes of the hyperbola x y 4x 8y 21 0 a c y x 2 and y x 6 y x 2 and y x 6 b d y x 2 and y x 6 y x 9 and y x 9

Use L H pital s Rule to evaluate the limit lim lnx x1 x 1

7 3 points Calculate two iterations of Newton s Method to approximate a zero of the function using the given initial guess f x x 3 x 1 4

2 3 points Find the x values at which f x 2 is not continuous Which of the discontinuities are removable Which of the discontinuities are nonremovable

Find the limit lim 3x sinx X T

Are these vectors u 2 1 0 v 3 2 5 w 9 13 25 linearly independent or dependent If they are independent or dependent what will be the scalars of this equation Ju v w 0

1 Find the Binomial series for 1 1 x a 12x 3 x 4 x 5 x b 1 2x 3x 4x 5x4 c 1 2x x x x x d 1 2x 3x 4x 5x4

3 The table below shows the number of prescription drug sales in billions since 1995 Prescription Drug Sales Years Since 1995 billions of USD 68 6 81 9 103 0 121 7 140 7 0 2 3 4 5 a Write an equation that best models the data b Find the prescription drug sales in billions for the year 2005

46 Ten persons compete in a race In how many ways can the 1st 2nd and 3rd place awards be distributed if only one person receives each award What is the formula O A C 10 3 OB P 10 3 O C P 3 10 D C 3 10

Suppose a savings and loan pays a nominal rate of 3 2 on savings deposits Find the effective annual yield if interest is compounded quartos The effective annual yield is Type an integer or a decimal rounded to the nearest thousandth as needed

36 lim 2 The limit 2n 81x O A 1 B 1 OC does not exist D 0

67 cos x cos y sin x sin y sin x sin y cos x cos y 0

Find the solution of the exponential equation as in Example 1 Enter your answers as a comma separated list 3x 1 27 X

Use the Laws of Logarithms to combine the expression log4 6 2 log4 9

Use the Change of Base Formula and a calculator to evaluate the logarithm correct to six decimal places Use either natural or common logarithm log 5

Exercise 3 Determine whether the solution of r 8r 0 satisfying z 0 0 and r 0 1 is periodic Justify your answer

Sketch the graph of the function by plotting points f x log x 23 X 2 2 2 1 y 4 2 f x log x 2 N 4 6 8 10 X y 41 2 2 0 4 6 8

Express the equation in logarithmic form a ex 3 b e y

6 f x VA at Hole s at 6a 6b 6c 6d 6e 6f lim x 0 lim x 3 lim x 2 lim lim x 2 x 3x x 3 x x 2 x 3 f x lim X178 f x f x f x f x f x X

Aaliyah Julio Dan and Miriam are each studying sets of data Aaliyah is working with 14 data pairs with a correla coefficient of 0 9 Julio is working with 13 data pairs with a correlation coefficient of 0 8 Dan is working with 10 d pairs with a correlation coefficient of 0 1 Miriam is working with 15 data pairs with a correlation coefficient of 0 2 which two data sets is a linear regression model reasonable Aaliyah s and Julio s data sets Julio s and Miriam s data sets O Dan s and Miriam s data sets Miriam s and Aaliyah s data sets

If f x x 3x 5 and g x x 2x which graph shows the graph of f g x

What is the solution of 4x100 x 2500 x 50 x 2 5 Ono solution

Alice s backyard is a rectangular piece of property that is twice as long as it is wide The total area of her yard is 1 00 m What is the approximate width of her backyard A w 11 2 m 15 8 m 22 4 m 44 8 m

Which equation shows a valid step in solving 3 2x 6 2x 6 0 O 3 2x 6 2x 6 0 3 2x 6 3 2x 6 3 O 2 2x 6 3 2x 6 o 3 2x 6 3 2x 6 3

Without using a calculator, find the exact value of the expression: 16cos²(30)+24csc²(45).

A cell culture contains 12 thousand cells, and is growing at a rate of r(t) = 2e0.18t thousand cells per hour. Find the total cell count after 3 hours. Give your answer accurate to at least 2 decimal places.

Which of the following functions is guaranteed by the Extreme Value Theorem to have an absolute minimum on the interval [-10, 10]? f(x)=x^ -1/3 h(x)=x-2 / x^2-4 g(x)=√2x i(x) = COSX

If θ=-11π/6 , then sin(θ) = cos (θ) = Give exact values. No decimals allowed!

Find the domain of the following rational function. R(x) =X / X-125 Select the correct choice below and fill in any answer boxes within your choice. A. The domain of R(x) is {x| (Type an inequality. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The domain of R(x) is the set of all real numbers.

Use the a, b, and c-sliders to graph the function f(x) =3/x+2 +1. Complete parts 1 through 3 below. Use the interactive figure to find your answer. Use the left and right arrow keys to move along a slider as needed. Part 1: What is the domain of the function? The domain is __ . (Type your answer in interval notation.)

Analyze the graph of the function. R(x)= x²+x-42/ x²-x-30 (a) What is the domain of R(x)? A. {x|x #0, x# -7, x#6 and x# - 5} B. (xlx #6 and x # -5} C. (xlx #0, x#6 and x # -5} D. All real numbers (b) What is the equation of the vertical asymptote(s) of R(x)? Select the correct choice below and fill in any answer boxes within your choice. A. x= (Use a comma to separate answers as needed. Type an integer or a fraction.) B. There is no vertical asymptote.

Complete the sentence below. If 7+5 i is a zero of a polynomial function of degree 5 with real coefficients, then so is

Find the domain of the following rational function. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain of H(x) is {x}. The domain of H(x) is the set of all real numbers.

Analyze the graph of the function. (a) What is the domain of H(x)? A. (xlx # 10 and x # - 10} B. (xlx #0, x4, x# 10, and x# - 10} C. {x|x #4, x# 10, and x# - 10} D. All real numbers (b) What is the equation the vertical asymptote(s) of H(x)? B. There is no vertical asymptote.

(a) What is the domain of R(x)? A. (xlx #0, x#3, and x # -4} B. (xlx #0, x-3, and x #4} C. (xlx #3 and x# - D. All real numbers (b) What is the equation of the vertical asymptote(s) of R(x)? Select the correct choice below and fill in any answer boxes within your choice. B. There is no vertical asymptote.

Find the pattern in the sequence and determine the 41st term. 21, 26, 25, 30, 29, 34, 33, 38, ...

Analyze the polynomial function f(x) = x³ + x² -2x. Answer parts (a) through (e). [Hint: First factor the polynomial.] (a) Determine the end behavior of the graph of the function. The graph of f behaves like y = for large values of |x|.

Use the remainder theorem to find the remainder when f(x) is divided by x-1. Then use the factor theorem to determine whether x-1 is a factor of f(x). f(x) = 2x³-4x² + 3x - 1 The remainder is ...