Find the inverse function (if it exists) of f(x) = ln (1-2x). If the function is not invertible, enter NONE. f-¹(x) = (Write your inverse function in terms of the independent variable x.)

Q: Find f(x+h)-f(x)/h for the given function . f(x)=x2+8x

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Q: Find the directional derivative of the function at P in the direction of v. 1 = √₂ (i+j) f(x, y) =…

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Q: Two cars start from rest at a traffic light and accelerate for several minutes. The graph shows…

A: Given :The velocity of the graph of Car A and car B is given in the graph.And we know that the graph…

Q: a ht C1 For the function f(x,y) = 4x² + 7y², find the following. a. b. f(x+h,y)-f(x,y) h…

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Q: What intervals must be considered for finding solutions to the inequality x > 5-º? C. 03 d. x 3 a.…

A: Follow the procedure given below.

Q: Verify that the indicated relation is an implicit solution of the given first order differential…

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Q: -1 Range of f -4 -5 -6 O (c) Describe the relationship between the graphs. Domain of 1 -81 Range of…

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Q: Find the area between the curves. x = -5, x=2, y = 2x² +5, y = 0 The area between the curves is…

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Q: Solve the given differential equation by undetermined coefficients. y" + 7y' + 6y = 18 y(x) = || X…

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Q: Use the power series f(x) = In (1-x) = -for-1sx<1, to find the power series representation for the…

A: The power series fx=ln1-x=-∑k=1∞xkk, for -1≤x&lt;1 we have to find the power series for px=9x8ln1-x

Q: 1 For the parametric curve * = find an equation for the tangent line to the curve at the point…

A: To find equation of tangent line:

Q: 3. A white wine at room temperature 70° F is chilled in ice (32°F). If it takes 15 minutes for the…

A: The solution is given below

Q: Write the given differential equation in the form L(y) = g(x), where L is a linear differential…

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Q: Write an equation for the function graphed below -7 -6 -5 y = 4 110 123 ku 3 4 5 6 a

A: We can  formulate the equation of the function by using the vertical asymptote and the  intercepts.

Q: 3. Find the equation of the tangent to the curve 3xy-y²= 7 at the point (.1).

A: Follow the procedure given below.

Q: n=1 [cos-²x dx] n 2. Derive the reduction formula for cos"x. [fcos"x dx= cos x sinxn- n

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Q: (a) Determine whether the series n=1 n+1 n³ +3 is convergent or divergent.

A: Solution: ∑n=1∞n+1n3+3

Q: Diminishing Returns Jesaki Inc estimates that it will sell N(x) units of product after spending $x…

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Q: The approximate rate of change in the number (in billions) of monthly text messages is given by the…

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Q: According to Fermat's Theorem: If f has a local maximum or minimum at c, and if f'(c) exists, then…

A: To give two examples (one of each) of specific functions f and values of c that demonstrate the…

Q: What is the gradient of f(x, y, z) = x³₂² + y³z +125z - 1 at P(5,5,-1) ? 75i + 75k -75i - 75k 75i -…

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Q: Find the limit of s(n) as n → ∞0. ( s(n) = 4 n n(n + 1)(2n + 1) 8

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Q: Show that the function f(x,y) = 8x²y subject to 3x - y = 9 does not have an absolute minimum or…

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Q: 3 Solve the following ODES by Inverse Operator method. 2X (D²³ +1) y = 3+* +52x ● X/2 Ans: y=c₁e³+…

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Q: Verify the identity. 1 - cos(a) sin(a) 1 - cos(a) sin(a) sin(a) 1 + cos(a) 1- cos(a) sin(a) 1 1 +…

A: Given,…

Q: Given that log a ( 2 ) = m and log a ( 3 ) = n , write exact expressions in terms of m and/or n for…

A: Write expression in terms of m and n for each of the following.

Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

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Q: 1. Let r(0) = 2sin(0) + cos(Ⓒ) be the polar definition of a planar curve. Find, in standard x-y…

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Q: Write an equation for the function graphed below 13- 12- 1 - 5+ ++ -7 -6 -5 -4 -3 -2 -2 1-1 HE A 1 2…

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Q: The holes cut in a roof for vent pipes require elliptical templates. A formula for determining the…

A: We need to find length and width.

Q: A box without a lid is required to have volume, V = 32000 cm^3. Minimize the amount of cardboard…

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Q: O O O O O IfE is the solid hemisphere a² + y² +2²5 49 and y 20, set up the integral using spherical…

A: Solution: In converting to spherical coordinates, we use so that

Q: Use the summation formulas to rewrite the expression without the summation notation. S(n): = 8i + 7…

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Q: Solve the given differential equation by undetermined coefficients. y" - y² + ²y = 2 + ex/2 y(x) =

A: The characteristic equation is            m2-m+14=0⇒4m2-4m+1=0⇒m=--4±02· 4⇒m=12,12 Now, the general…

Q: Evaluate the following expressions. Your answer must be an exact angle in radians and in the…

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Q: ƒx(2x−1) dx 2 √x³√x²+4 dx

A: for (1),     ∫ x2x-17dx=∫ 128x8-448x7+672x6-560x5+280x4-84x3+14x2-xdx=∫ 128x8dx-∫ 448x7dx+∫…

Q: Analyze the following graph of f'(x). Select all of the intervals over which f(x) is concave down.…

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Q: 2) y" - y' — 6y = 0. бу

A: Follow the procedure given below.

Q: 1) Solve the following ODES by Undetermined Coeff. ● 4X 11 X y - 16 y = 19.2 € + 60e, y(a) = y() -4X…

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Q: For So √ 1² dt. use a change of variables to evaluate the definite integral. √5+t²

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: cook Use the power series f(x) = In (1-x) = - Σ for -15 x <1, to find the power series…

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Q: Solve the differential equation by variation of parameters. 1 8 + ex y" + 3y' + 2y = Step 1 We are…

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Q: 9-x2 x dx

A: ∫9-x2x2dx=∫cot2udu=∫ -1+csc2udu=-∫ 1du+∫csc2udu=-u-cotuSubstitute back…

Q: Find and graph the level curve of the function g(x,y)=x^2+y^2-6x+2y corresp

A: the answer is given in step2

Q: 8. A rocket is fired into the air with an initial velocity of 98 m/s. The height (h) of the rocket…

A: The height of the rocket after t seconds is given by the expression h=98t-4.9t2

Q: PLEASE

A: As per policy only first question is answered. Please refer to the image below

Q: Evaluate the limit lim_ (8x² + 4) (6x + 8 →7

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Q: all company of science writers found that its rate of profit (in thousands of dollars) after t years…

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Q: Evaluate the definite integral: f (x · cos(2x)) dx. Enter the exact decimal value. A graph of y = x…

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