Find functions f and g so that fog=H. 9 H(x) = (9x + 6) Choose the correct pair of functions. ..

Q: Find the domain of f(x). f(x) = Interval 3x - 5 x² + 2x - 35 Answer Attempt 1 out of 2 2 Answer…

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Q: Find a, b, c, and d such that the curve ?=??3+??2+??+? has its tangent line at(1, 1) and at (0, -2)…

A: The objective of this question is to find the coefficients a, b, c, and d of the cubic function y =…

Q: Find the average rate of change between x = 1 and x = 5 for the function shown in the table below. X…

A: x−5−4−3−2−1012345f(x)4734231472−1−2−127Average rate of change of f(x) on [a,b] is Average rate of…

Q: Find an antiderivative of the function g(t) = e-³t. An antiderivative is

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Q: number. Fr 11. The sum of the measures of the three angles of a triangle is 180°. The middle-sized…

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Q: 19. If $100,000 is invested at 6% compounded monthly for 7 years, the compounded amount is given by…

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Q: Determine lim f(x) given the definition of f(x) below. (If the limit does not exist, enter DNE.)…

A: For finding, if f(x) is a polynomial, then for finding limit, we need to substitute a in f(x) and…

Q: Find the unit tangent vector T(t) at point P. r(t) = t²i + tj + 20 k, T(5)= X P(25, 5, 20/3) Find a…

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Q: What is the second derivative x³ - 5x² + x = 0? A. 3x² - 5x B. 10x-5 C. 3x + 10 D. 6x-10

A: The given equation is Let

Q: Given the definitions and g(x) below, find the value of f(g(−3)). of f(x) 2 f(x) = x² + 7x + 13 g(x)…

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Q: Let f(x) = 3x - 6 and g(x)=x+3. Find each composite function and describe the domain of the…

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Q: Suppose f(x) = 3x -2. Find f (x+²) 3 (x+2) 3 (Simplify your answer.)

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Q: Find the indefinite integral. fett 7t dt = +C

A: I=∫e7tdt

Q: 8. An engineer invests $27,000 in two bonds. If one 7% and the other yields 9%, how much is invested…

A: Let engineer invest $x on one bond which yields and  on another bond which yields

Q: 5. If f(5) = 7.8 and ƒ' (5) = 5.2, then use the linear approximation (also called the tangent line…

A: The linear approximation of a function f(x) at x=a is given by

Q: 17. Determine whether the sequence converges or diverges. Find the limit if converges: a = 2n+3 2n+1…

A: To determine whether the sequence converges or diverges.To find the limit if it converges.

Q: Question 14 You have been given the following signal (shown below). What is its laplace transform?…

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Q: Consider the function f that is continuous on the interval [-3, 3] and for which the following is…

A: Given that f is a continuous function on the interval  and To find:-(f is even) (f is odd)

Q: Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an…

A: The objective of this question is to find the relative extrema of the function f(x) = sqrt(25 - x^2)…

Q: Determine the x values where the following function is discontinuous Select all correct answers.…

A: The given function,The aim is to find the discontinuous points of the function .

Q: d) Write an expression that represents the approximate value of g(x) for a generic value x in the…

A: The graph of the function g'(x) is shown as,

Q: 256x The volume of a sphere is increasing at a rate of 3 cm³/sec. Find the rate of change of its…

A: The expression for the surface area of the sphere is:Where r is the radius of the sphere.The…

Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WORK FOR BETTER…

A: The given integral is

Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region…

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Q: Let y = f (x) be the particular solution to the differential equation with the given initial dy dx…

A: The given initial condition is .The aim is to find the tangent line to approximate to .

Q: Find the integral. Use C for the constant of integration. | (x² (y² + 3)² dy

A: The objective of the question is to find the integral of the given function with respect to y. The…

Q: Use the test-point method to solve the polynomial inequality. x³ - 6x² ≥0

A: By using the test-point method to solve the following polynomial inequality.

Q: Given the definitions of f(x) and g(x) below, find the value of (fog)(2). f(x) g(x) = X = -x+ 2 2 _…

A: Given:

Q: (a) Find a power series representation for f(x) = (b) Use your answer in part (a) to evaluate the…

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Q: Use the graph to evaluate the limit. lim f(x) X→-1 X G

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Q: 9. Find the interval of convergence of the series: 2¹ (x + 3)¹ In(n) ∞ n=2

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Q: (c) (d) (e) creasing? Does g(x) have any critical points? If any, identify all critical points. On…

A: Given: To Find: (c) To find the critical points if any of g(x).(d) To find the interval(s) on which…

Q: Let f(x) = x if x ≥ 5 5 if x < 5 a. Find f(1), f(5), and f(7). b. Sketch the graph of y = f(x).

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Q: Find all the antiderivatives of the following function. Check your work by taking the derivative.…

A: Given,

Q: Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the…

A: The standard form equation of the vertical parabola:Where  is the coordinate of the vertex of the…

Q: Biologists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population…

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Q: Question 12 Determine the value of x(t) at t = 0 given its Laplace transform. Choose your answers…

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Q: The amount, A, of 159 grams of a certain radioactive material remaining after years can be found by…

A: Given that the amount A of 159 grams of a certain radioactive material remaining after t years is

Q: Find the indefinite integral. (8x + 2) dx = = +C

A: We know that,.Let assume,

Q: Consider the following function. g(x) = (x - 2)²-9 Step 3 of 4: Find two points on the graph of the…

A: Consider the function

Q: Find the limit as a number, ∞o, or -∞o. Otherwise enter DNE. lim [√(√An+1 = √an)] = [ 4n n→ ∞o

A: Limn-infinity [sqrt(n) (sqrt(4n+1)-sqrt(4n))]

Q: Evaluate the indefinite integral. [(arcsin x)² √1-x² -dx

A: We have given indefinite integral-First let's define that-

Q: The equation of a hyperbola is 64 a) Find the center, vertices, transverse axis, and asymptotes of…

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Q: Consider the following function. f(x) = -5x Complete the table.

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Q: Write the expression as a sum and/or difference of logarithms. Express powers as factors. In…

A: Let, .We know that,

Q: them by mteger values. For each of the following logarithmic expressions, give the two integers that…

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Q: Find an equation of the tangent line to the graph of the function at the given point. y = 4 − x² −…

A: y=4−x2−ln⁡(12x+1), point (0,4)

Q: For f(x) = √10-2% @ Find the domain. Write answer in internal notation 6 Graph f(x) = √10-22.…

A: Domain: The set of values for which a function f(x) is defined is called the domain of the…

Q: Find the area of the region enclosed by the curves between their intersections. y=x² and y= 2x

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Q: 1. Find the area bounded by x = y²; x = −2y² +3

A: To find the area bounded by