Verify that the following functions are inverses of each other. Clearly show the proofs! f(x)=2e1x+4 and g(x) = 1 - In (x-4) 2

Q: G=4/5 - 1/3 x 2/15 + 4/45

A: We need to find value of G.

Q: Use implicit differentiation to find y' for 5x³y² + In (xy²) = 5 and then compute y' at (1, −1).…

A: Answer ::The final answer is 1211​Explanation:sol) Hence,The final answer is1211​

Q: The Parametric equation of the line that passes through the point A(1, -1, 1) and parallel to the…

A: Given that line passes through the point A(1,−1,1) and parallel to vector v→(1,0,1)To find:…

Q: Evaluate the integral L 4 diverges. 2 3x ln x dx or state that the integral

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Q: We'll be analyzing the surface area of a round cylinder - in other words the amount of material…

A: The domain of A(r) represents the valid value for the radius r for which the function A(r) is…

Q: For the function g(x) graphed here, find the following limits or explain why they do not exist. a.…

A: The condition of existence of the limit at

Q: Find all points where the function is discontinuous. 6 4 2- X 2 6 18 Q OA. x=2 and x = 4 OB. x=2 OC.…

A: As  is included in the domain   : Defined Function is continuous at x=2

Q: 3. Use the method of shells to calculate the volume that is created when the following area is…

A: The exact volume is 92π(sin3−3cos3​ which is approximately equal to 2.17.Explanation:Steps and…

Q: A spherical balloon is inflating with helium at a rate of 80x ft³/min. How fast is the balloon's…

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Q: Find the following derivatives by using the product rule and/or the chain rule: (You can use the…

A: As per the Bartleby answering guidelines, answering only first question as the other questions are…

Q: A. Find the equation of the line that passes through the points A(1,-1,1), B(1,2,0).

A:

Q: Find the equation of the tangent line to the function f(x) = In(6x) at x = 6. (Use symbolic notation…

A: f(x)=ln⁡(6x) at x=6f′(x)=ddxln⁡(6x)Using the chain…

Q: Vector-valued functions (VVF) VVF Point P t value (for point 1 r(t) = ½ t²i + √4 − t j + √t + 1k (0,…

A: To solve the problem, I'll write MATLAB (Octave compatible) code to plot the vector-valued function…

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: (a)f(6)=4(b)limx→2​f(x)= Do Not Exist.(c)limx→6​f(x)=2(d)limx→2−​f(x)=1Explanation:Step 1:Step 2:…

Q: 7) Find the derivative of x(x) = (2x+3)³ (2x+3)+2x+4 X + √ 7

A: Given that, we have to find the derivative of y(x).

Q: Plot the points from the table below on the polar grid that follows.

A: Plot the points from the table below on the polar grid that follows.Explanation:To plot a point in…

Q: ||| = 19:25 0% * · Natifa Hinds Today, 18:08 3. Tesla estimates that its profit expressed in…

A: Tesla's variable cost per car is $3210. Explanation:a. Tesla's Variable Cost per Car:Given that…

Q: Let a <b. Let f be a continuous function on [a, ∞o). Prove that the following two statements are…

A: The document proves that the following statements are equivalent:The improper integral ∫ from a to…

Q: Assuming that the domain of the function is the largest possible subset of R (the set of real…

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Q: X+2 At what points is the function y = continuous? x²-11x+18 Describe the set of x-values where the…

A: Given function is We have to find the points where the given function y is continuous.

Q: NOTE: When using interval notation in WeBWorK, remember that: You use 'INF' for ∞ and '-INF' for -∞.…

A: a) concave up  DNE    Concave down (-inf , inf)b). DNEc) Relative Maximum x=-1     Relative minimum.…

Q: dx Assume that x = x(t) and y = y(t). Let y=x3+2 and =5 when x=3. dt dy Find when x=3. dt dy…

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Q: Examine the function and a A point C1 y= -Incx)

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Q: Use the arc length formula to find the length of the curve y=9-4x,-2 ≤ x ≤ 4. Check your answer by…

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Q: Find the derivative of f with respect to x of f(x) = In x 12

A: The objective of the question is to find the derivative of the function f(x) = ln(x^12) with respect…

Q: Find the directional derivative, Dчf, of the function at the given point in the direction of vector…

A: Therefore, the required answer is Du​f(2,3)=0Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Determine the limit by sketching an appropriate graph. √1- 0sx < 1 lim f(x), where f(x)= X-1 1 1sx <…

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Q: lim n!en 1/2

A: √(2π) Or. √2 •. √πExplanation:Step 1: Step 2: Step 3: Step 4:

Q: Next Suppose the Sunglasses Hut Company has a profit function given by P(q) = -0.03q2 + 3q- 44,…

A: Given:a profit function given by P(q)=−0.03q2 +6q−48 where q is the number of thousands of pairs of…

Q: what's the final answer to a and b?

A: The objective of the question is to find the moment of time t0 and the point P0 on the curve r(t)…

Q: Use the table of values of f(0) = cos (40) 0 to estimate lim f(x), if it exists. 0-0 0 -0.1 -0.01…

A: From the definition of limit, limit does not exist when the left hand limit and right hand limit is…

Q: dy Use implicit differentiation to find without first solving for y. dx -16x³ + 4x16y+y₁ = 77

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Q: If f(x) = 7 sin(2x) arcsin(x), find ƒ'(x).

A: f′(x)=14cos(2x)arcsin(x)+1−x2​7sin(2x)​Explanation:Given function is  f(x)=7sin(2x)arcsin(x) We need…

Q: Find the values of x, y and z that correspond to the critical point of the function: f(x, y) = 4x² -…

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Q: Consider the following curve. f(x) =  x − 4 x2 Determine the domain of the curve. (Enter…

A: The objective of the question is to analyze the curve f(x) = (x − 4) / (x^2) in terms of its domain,…

Q: Find the maximum and minimum values of f(x, y) = xy on the ellipse 32+ y² = 5. maximum value =…

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Q: Find the points on the surface 5x² + 1y²+4z² = 1 at which the tangent plane is parallel to the plane…

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Q: A. Find the equations of the intersection line between the planes 3x + y z = 2 and x-y+2z = 3

A: Given two equations of planes3x+y−z=2 and x−y+2z=3To find: equations of the intersection line…

Q: ​(A) Find the instantaneous rate of change of the amount in the account after 1 ​year(s)? (B) Find…

A: The required answers are A) 925.409507 dollars per year.B) 935 dollars per year.Explanation:Step 1:…

Q: Let an and ag = 9. n+1 a) Determine whether the given equation is explicit or recursive. The…

A: Recursive means a function that repeats or uses its own previous term to calculate next terms forms…

Q: If [5 - -8 A = [611] 0 " then A- 1 =

A: The objective of the question is to find the value of 'A - 1' given the equation '5 - -8A = 611'.

Q: Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve…

A: Given that the region is bounded by the curve The surface area of the revolution about the x-axis of…

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: Question 15a. The initial population is 450.b. The population of the colony at 5 hours is 1725.c.…

Q: 140 CHAPTER 3 Functions tab B 49. Let f(x) = (x - a)/(x + a). (a) Find f(a), f(2a), and f(3a). Is it…

A: f(a)=0f(2a)=1/3f(3a)=1/2Explanation:Hope it helps youplease ask if you gets any doubtplease give…

Q: I need help with 45.

A: (45) We have proved that, f(a+b)=f(a)+f(b)Function : f(x)=x2−1 Example : f(2+3)=f(2)+f(3)⇒24=11So,…

Q: Let f(x)=3x³-5x²-2, x≥ 1.5. Find the value of df at the point x=248 = f(5). dx df The value of dx 1…

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Q: Problem #1: By Taylor's theorem, we can find a Taylor polynomial P3(f) of degree 3 for the function…

A: Given: To Find: To calculate the coefficient .

Q: #14. Given the integral SS² y² cos xdxdy (a) Evaluate it. "(with the given order of integration),…

A: a.)∫12​∫02π​​y2cos(x)dxdy=∫12​[y2sin(x)∣x=0x=2π​​]dy=∫12​[y2sin(2π​)−y2sin0)]dy=∫12​[y2⋅1−y2⋅0]dy=∫1…

Q: C. Find the equation of the plane that passes through the points A(1,-1,1), B(1,2,0) and C(0,1,-1)

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Q: Use undetermined coefficients to find the particular solution to y"-3y-10y=4e³t Yp(t) =

A: