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study help
mathematics
college mathematics for business economics
Questions and Answers of
College Mathematics For Business Economics
Find the indicated derivatives in Problems 33–56. h' (t) if h(t) = 3 13/5 6 1¹/2
In Problems 50 and 51, approximate (to four decimal places) the value(s) of x where the graph of f has a horizontal tangent line. f(x) = x³10x³ - 5x + 10
In Problems 51–66, find each indicated quantity if it exists. Let f(x) = (1-x² [1 + x² (A) lim f(x) x-0 (C) lim f(x) if x ≤0 if x > 0 . Find (B) lim f(x) x-0 (D) f(0)
In Problems 51–66, find each indicated quantity if it exists. √2 + x (2 - x Let f(x) (A) lim f(x) (C) lim f(x) x-0 if x ≤ 0 if x > 0 Find (B) lim f(x) x 0 (D) f(0)
In Problems 51–64, find all horizontal and vertical asymptotes. = +1 x²2²-1 X
Find the indicated derivatives in Problems 33–56. y' if y || 1 Vx
Find the indicated derivatives in Problems 33–56. w' if w w= 10 15
A rat moves along a wall (scale in feet) so that at time x (in seconds) it is at height y = -3x2 + 50x + 10. Find(A) The instantaneous velocity function (B) The velocity at time x = 2 seconds.
In Problems 51–64, find all horizontal and vertical asymptotes. = x³ 1² +6
Find the indicated derivatives in Problems 33–56. d 1.2 dx √x 3.2x 2 + x
Use the graph of f to determine where Express answers in interval notation. (A) f(x) > 0 (B) f(x) < 0
In Problems 55–59, determine where f is continuous. Express the answer in interval notation. f(x) = x + 1 x-2
Given f(x) = x2 - 4x,(A) Find f'(x). (B) Find the slopes of the lines tangent to the graph of fat x = 0, 2, and 4. (C) Graph fand sketch in the tangent lines at x = 0, 2, and 4.
In Problems 55–59, determine where f is continuous. Express the answer in interval notation. f(x) = x +4 2 x² + 3x - 4 X
In Problems 55–59, determine where f is continuous. Express the answer in interval notation. f(x) = √4-x²
In Problems 55–59, determine where f is continuous. Express the answer in interval notation. f(x) = √4x² -
In Problems 60–69, evaluate the indicated limits if they exist. Let f(x) = 3x x² - 7x (A) lim f(x) x 2 Find (B) lim f(x) (C) lim f(x) x-0
In Problems 60–69, evaluate the indicated limits if they exist. Let f(x) (A) lim f x + 1 (3 - x)²* Find (B) lim f(x) x--1 (C) lim f(x)
In Problems 61–66, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If f(x) = C is a constant function, then f'(x) = 0.
In Problems 61–66, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. = m. If f(x) = mx + b is a linear function, then f'(x) =
In Problems 51–64, find all horizontal and vertical asymptotes. f(x) 2x² + 7x + 12 2x² + 5x12
In Problems 51–64, find all horizontal and vertical asymptotes. f(x) = 2x²5x + 2 x² - x - 2
In Problems 60–69, evaluate the indicated limits if they exist. x - 3 9 - x² Let f(x) (A) lim f(x) Find (B) lim f(x) x--3 (C) lim f(x) x-0
In Problems 60–69, evaluate the indicated limits if they exist. Let f(x) = x²-x-2 7x + 10 +² (A) lim f(x) Find (B) lim f(x) (C) lim f(x)
In Problems 61–66, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If a function f is differentiable on the interval (a, b), then
In Problems 60–69, evaluate the indicated limits if they exist. Let f(x) = 3x (A) lim f(x) x-x 2x - 6 Find (B) lim f(x) 8114 (C) lim f(x) x-2
In Problems 61–66, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.The average rate of change of a function f from x = a to x = a
In Problems 60–69, evaluate the indicated limits if they exist. Let f(x) = 2x³ 3(x - 2)2 (A) lim f(x) x →∞0 Find (B) lim f(x) x--∞ (C) lim f(x) x-2
In Problems 60–69, evaluate the indicated limits if they exist. Let f(x) = 2x 3(x - 2)³* (A) lim f(x) x-x Find (B) lim f(x) X118 (C) lim f(x)
In Problems 61–66, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If the graph of f has a sharp corner at x = a, then f is not
In Problems 60–69, evaluate the indicated limits if they exist. f(x + h) - f(x) h lim h→0 for f(x) = 1 x + 2
In Problems 70 and 71, use the definition of the derivative and the four-step process to find f′(x). f(x) = √x - 3
In Problems 67–72, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If f is a function such that lim f(x) exists, then
In Problems 73–80, is the limit expression a 0/0 indeterminate form? Find the limit or explain why the limit does not exist. (x-7)² 7x² - 4x - 21 lim x→7x2²
In Problems 73–76, give a pair of limit expressions that describe the end behavior of the function. f(x)= x³ 3x + 1
In Problems 73–80, is the limit expression a 0/0 indeterminate form? Find the limit or explain why the limit does not exist. x-5 lim x 2x + 2
In Problems 71–76, determine whether f is differentiable at x = 0 by considering lim h→0 f(0 +h)-f(0) h
In Problems 73–80, is the limit expression a 0/0 indeterminate form? Find the limit or explain why the limit does not exist. lim x-4(x + 4)² x² + 4 2
In Problems 73–76, give a pair of limit expressions that describe the end behavior of the function. f(x) 2+5x 1- x
In Problems 71–76, determine whether f is differentiable at x = 0 by considering lim h→0 f(0 + h)-f(0) h
In Problems 73–80, is the limit expression a 0/0 indeterminate form? Find the limit or explain why the limit does not exist. lim x-9 rẻ – 5x – 36 x 9
In Problems 73–76, give a pair of limit expressions that describe the end behavior of the function. f(x) 9x² + 6x + 1 4x² + 4x + 1
In Problems 73–80, is the limit expression a 0/0 indeterminate form? Find the limit or explain why the limit does not exist. 1² + 36 x lim x6 x + 6
Find the indicated derivatives in Problems 77–82. 2 = (2x - 1)² f'(x) if f(x) =
In Problems 77–82, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.A polynomial function is continuous for all real numbers.
In Problems 73–80, is the limit expression a 0/0 indeterminate form? Find the limit or explain why the limit does not exist. lim x-10 x² - 15x + 50 (x - 10)²
Find y' for y = y(x) defined implicitly by the equation y4 In x + 2x + 8 = 0, and evaluate at (x, y) = (1, 1).
In Problems 9-12, find y' in two ways:-2x + 6y - 4 = 0(A) Differentiate the given equation implicitly and then solve for y′. (B) Solve the given equation for y and then differentiate directly.
In Problems 9-34, find f'(x) and simplify.f(x) = 5x2 (x3 + 2)
Use a calculator to evaluate A to the nearest cent in Problems. A = $5,000e0.08r for t = 1, 4, and 10
In Problems 9–14, find the relative rate of change of f(x).f(x) = 60x - 1.2x2
In Problems 9-14, assume that x = x(t) and y = y(t). Find the indicated rate, given the other information. x² + y² = 1; dy/dt find dx/dt = -4 when x = -0.6 and y = 0.8;
In Problems 9-12, find y' in two ways:3x2 - 4y - 18 = 0(A) Differentiate the given equation implicitly and then solve for y′. (B) Solve the given equation for y and then differentiate directly.
Given the demand equation 25p + x = 1,000, (A) Express the demand x as a function of the price p. (B) Find the elasticity of demand, E(p). (C) Find E (15) and interpret. (D) Express the revenue
Find the slope of the line tangent to y = 2 ln(x + 2) + 5e-³x when x = 0.
In Problems 9-12, find y' in two ways:2x3 + 5y - 2 = 0(A) Differentiate the given equation implicitly and then solve for y′. (B) Solve the given equation for y and then differentiate directly.
In Problems 9-34, find f'(x) and simplify. f(x) X x - 3
In Problems 9–14, find the relative rate of change of f(x).f(x) = 15 - 3e-0.5x
In Problems 9-14, assume that x = x(t) and y = y(t). Find the indicated rate, given the other information. x² + 3xy + y² = 11; dx/dt = 2 when x = 1 and y = 2; find dy/dt
In Problems 13-30, use implicit differentiation to find y' and evaluate y' at the indicated point.y - 5x2 + 3 = 0; (1, 2)
In Problems 9-34, find f'(x) and simplify. f(x) = 3x 2x + 1
In Problems 13–18, solve for t or r to two decimal places.2 = e0.06t
Find the indicated derivatives in Problems 14–19. [ 2 2 ] + 2 ( 2 ण) ] 2p P
In Problems 73–80, is the limit expression a 0/0 indeterminate form? Find the limit or explain why the limit does not exist. 8 - x lim x8x² +8x² - 64
In Problems 77–82, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If f is a function that is continuous at x = 0 and x = 2, then
Find the indicated derivatives in Problems 77–82. d 10x + 20 dx X
In Problems 78–82, find all horizontal and vertical asymptotes. f(x) = x² + 9 x-3
In Problems 73–80, is the limit expression a 0/0 indeterminate form? Find the limit or explain why the limit does not exist. x + 3 lim x3x3
Find the indicated derivatives in Problems 77–82. dy dx if y x² + 25 好
In Problems 77–82, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If f is a function that is continuous on the open interval (0,
In Problems 78–82, find all horizontal and vertical asymptotes. f(x) ²-9 x² + x - 2
A company’s total sales (in millions of dollars) t months from now are given by (A) Use the four-step process to find S' (t). (B) Find S(15) and S' (15). Write a brief verbal interpretation of
Find the indicated derivatives in Problems 77–82. dy dx if y || 3x - 4 - 12x²
In Problems 78–82, find all horizontal and vertical asymptotes. = 1³-1 x³x²-x+1
Find the indicated derivatives in Problems 77–82. f'(x) if f(x) 2x³ -4x² + 2x 1³
The U.S. consumption of tungsten (in metric tons) is given approximately byWhere t is time in years and t = 0 corresponds to 2010. (A) Use the four-step process to find p′(t). (B) Find the annual
In Problems 83–86, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. The derivative of a product is the product of the
In Problems 83–86, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. The derivative of a quotient is the quotient of the
In Problems 83–86, sketch a possible graph of a function f that is continuous for all real numbers and satisfies the given conditions. Find the x intercepts of f. f(x) < 0 on (-∞, -6) and (-1,
In Problems 83–86, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. The derivative of a constant is 0.
First-class postage in 2009 was $0.44 for the first ounce (or any fraction thereof) and $0.17 for each additional ounce (or fraction thereof) up to a maximum weight of 3.5 ounces.(A) Write a
In Problems 83–86, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. The derivative of a constant times a function is 0.
A company’s total sales (in millions of dollars) t months from now are given by(A) Find S' (t). (B) Find S(4) and S' (4) (to two decimal places). Write a brief verbal interpretation of these
In 1913, biochemists Leonor Michaelis and Maude Menten proposed the rational function model (see figure)for the velocity of the enzymatic reaction v, where s is the substrate concentration. The
In Problems 5–8, find the indicated derivative. d dx (In x³ + 2e)
In Problems 5-8, find functions E(u) and I(x) so that y = E[I(x)]. y = ln (x³ - 6x + 10)
In Problems 5–8, find the indicated derivative. d dx -e2x-3
In Problems 5-8, find functions E(u) and I(x) so that y = E[I(x)]. y = (2x9)8
Find the probabilities in Problems 7–12 by referring to the tree diagram below. Start .6 .4 M N .8 .2 .3 .7 -A -B A - B
Find the probabilities in Problems 17–22 by referring to the following tree diagram and using Bayes’ formula. Round answers to three decimal places.
In Problems 2–6, P is a transition matrix for a Markov chain. Identify any absorbing states and classify the chain as regular, absorbing, or neither. P= A А А .4 в 1 B .6 0
In Problems 2–6, P is a transition matrix for a Markov chain. Identify any absorbing states and classify the chain as regular, absorbing, or neither. A B A 1 0 0 1 .30 P = B с с 0 0 .7
In Problems 2–6, P is a transition matrix for a Markov chain. Identify any absorbing states and classify the chain as regular, absorbing, or neither. P= B B C D 0 0 0 1 0 0 4 0 0 D.15
In Problems 7–10, write a transition matrix for the transition diagram indicated, identify any absorbing states, and classify each Markov chain as regular, absorbing, or neither.
Given the transition matrix Find the probability of (A) Going from state B to state A in two trials. (B) (B) Going from state A to state B in three trials. P= A А A | 7 BL. .1 B .3 .9
A Markov chain has four states, A, B, C, and D. The probability of going from state A to state B in one trial is .3, the probability of going from state A to state C in one trial is .4, the
In Problems 15 and 16, find the limiting matrix for the indicated standard form. Find the long-run probability of going from each nonabsorbing state to each absorbing state and the average number of
In Problems 22 and 23, determine the long-run behavior of the successive state matrices for the indicated transition matrix and initial-state matrices. A B 0 0 1 C2 A P = B (A) So (B) So C 1 0
Let P be a 2 × 2 transition matrix for a Markov chain. Can P be non-absorbing if two of its entries are 0? Explain.
Let P be a 3 × 3 transition matrix for a Markov chain. Can P be regular if three of its entries are 0? If four of its entries are 0? Explain.
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