If the tangent line to y = f(x) at (6, 3) passes through the point (0, 2), find f(6) and f'(6). f(6)= f'(6) = X

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Q: Suppose you want to start saving for retirement. You decide to continuously invest $25000 of your…

A: Given P = 25000 r = 6%

Q: əz Use the chain rule to find and Əs дz Əs дz at || n(=), z = tan əz at u = 5s + 9t, v = 9s - 5t

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Q: 11. Let f(x) = x³ - 2x² + x-1 so f(1) = -1 and f(2)= 1. Let g be the X inverse of f; that is, g(x) =…

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Q: Find the sum of the given vectors. a = (2, -3), b = (-1,7) Illustrate geometrically. O y a+b y a+b…

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Q: (12) Find the equation of the line passing through the point (1,4) that is perpendicular Y x to the…

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Q: Solve the initial value problem using auxillary equation 22. y" + 2y' +17y=0; y(0) = 1, y'(0) = -1

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Q: 8. y=(x-2)², y = x + 10; about the x-axis

A: Given y = ( x - 2 )2 y = x + 10 about x axis

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Q: Solve for the exact value of the variable in each of the following equations. a. b. 8e+-3x = 11…

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Q: B. lim x-00 8x47x² +50 4x4 100x³ + 13x

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Q: Current Attempt in Progress For g(x)=x² + 3x + 2, find and simplify g(4+h)- g(4). g(4+h)-g(4) =

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Q: 4 5g fg 25 y.fig 14841551-800 = 8.162-8.02 0.142 = 0.1 2 decimal Sig. fig what does that mean? I got…

A: We will use concept of significant figure and rounding off.

Q: Given that f(x) = 9x + 7 and g(x) = 1 - x², calculate (a) f(g(-4))= (b) g(f(-4))=

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Q: Let f(x) = 4x +3 and g(x) = 2x² + 5x. After simplifying, (fog)(x) =

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Q: Use the graph of the function f shown to estimate the indicated quantities to the nearest integer.…

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Q: Find the marginal profit function if cost and revenue are given by C(x) = 207 +0.4x and R(x) = 4x…

A: Let's find marginal profit function.

Q: Write the exponential function y = 400e-0.11t in the form y = Pat. (a) Once you have rewritten the…

A: given exponential function: y=400e-0.11t.........(1)

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Q: find the the derivative of f(x) = (3/4x)^6

A: Topic - Derivative of a function We are given  f(x) = 34x6 we know thatddxxn=nxn-1

Q: a) Use the Product Rule to find the derivative of the given function. b) Find the derivative by…

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Q: If f(x)=12pi^7, then what is f'(x) equal to?

A: We are given  f(x) = 12pi^7 derivative of constant is zero

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Q: 7. A force of 10 lb is required to hold a spring stretched 4 in. beyond its natural length. How much…

A: Given Force( F ) = 10 lb xinitial = 4 in xfinal = 6 in

Q: calculate the volume of the shape obtained by rotating the region bound by f(x)=x/4 and g(x)=…

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Q: K Find and simplify the expression if f(x) = x² – 3. f(x + 1) f(x+1)= (Simplify your answer. Use…

A: Given query is to find the Indicated function value.

Q: Given y = 5e³ + sin(x), OOOO 2.667e³-cos(x) 15e³ + cos(x) 15e³ - sin(x) dy dx 5e³ + cos(x)

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Q: 3. (1+4e3x)³ e3x dx

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Q: K Let f(x) be a differentiable function such that f(4) = 3 and f'(4) = 5. If g(x)=x².f(x), then find…

A: The objective is to solve the above question.

Q: -x) dx Answer Solid obtained by rotating the region 0 < x < 1, ³ < y ≤ x² about the x-axis

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Q: let f(x) be the function 12x^2-2x+7. Then the quotient (f(6+h)-f(6))/h can be simplified to ah+b…

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Q: _4. y=e*, y=0, x=-1, x = 1; about the x-axis

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Q: Let f(x, y) = x³ + 2y²x + y³ + 2x, then a) the gradient Vf(xo, yo) is equal to the null vector at a…

A: Given: let f(x,y)= x3+2y2x+y3+2x

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: Find the limits in a) through c) below for the function f(x) = OA. a) Select the correct choice…

A: We have to find the limit

Q: Evaluate the function f(x) at the given numbers (correct to six decimal places). x² - 8x f(x) = x²…

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Q: Find c such that the function f(x) = {2x-3 z>c I 1≤c M C is continuous everywhere.

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Q: e20 sin 30 de

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Q: Given f(x) = 4 sin x cos x, find f'(x). f'(x) =

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Q: Using the Quadratic Equation, solve the following for X: 4X² + 5X+6=0

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Q: Find the product and simplity it possil ((r-q)^(2))/(5r+5q)*(5r)/(r^(2)-rq)

A: let  D=(r-q)2(5r+5q)×5r(r2-rq)

Q: Let y=10/12x Power functions can be written as y=kx^p k= p=

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Q: Find y' by (a) applying the Product Rule and (b) multiplying the factors to produce a sum of simpler…

A: To find the derivative.

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: Sketch of the region: It is forming a disc. So disc method is used.