For the function h(t) = -t – 1, evaluate h(t) + h(2).

Q: Find the convolution f (t ) *g(t) f(t)=t,g(t)=1

A: By definition of convolution we have

Q: Let f (x) = x3 – 3x2 – 1, x 2 2. Find the value of df-1 at the point x = -1 = f (3). dx -

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Q: Find the antiderivative F(x) of f(x)=x/3(12x2-6), given F(1)=5

A: An anti derivative of a function f is a differentiable function, whose derivative should be equal to…

Q: 1+х f[X_, Y_] := 2 у - 1-x (1+) (у-1)2

A: We will use basic knowledge of the functions of several variable theory to answer this question.  We…

Q: For the function f(x.y) = e 4xy, find f, and f,. f, =

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Q: Show that, for any constant k, f(x)' dxL k f'(x) k

A: To show: For any constant k, ddxf(x)k = f'(x)k

Q: Estimate the IROC for the function f(t) =Ax) = x² – 20x

A: Given: fx=x2-20x To find the instant rate of change, Differentiate the given function with respect…

Q: For the following exercises, use the second derivative test to identify any critical points and…

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Q: Find Fxxygy for the function Fory)-J*J€nx-x]

A: We havr to find the derivative.

Q: Find the antiderivative F(x) of f(x)=x(2x+7), given F(4)=5

A: Given:The function is f(x) = x(2x+7), F(4) = 5.

Q: 3x2 Given that F(x) = In t dt, what is F'(x)? 3x 4 + t2 ||

A: Given, Fx = ∫3x3x2lnt4+t2dt  We have to find F'x.

Q: For the function y = f(x) = x² – 3x − 4, x ≥ 1.5, find df dy y=2

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Q: For the function f(x,y) = 8x² + 7y², find f(x + h,y)-f(x,y) = h f(x + h,y)-f(x,y) h

A: Given, f(x,y)=8x2+7y2

Q: Describe the long run behavior of f(t) = 4 1 As t → 0, f(t) → As t → 0, f(t) → ? v

A: We xan solve as follows

Q: Find for the following function. dx2 y=e -6x2 %3D dx2

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Q: For the function y = f(x) = x² − x + 5, x ≥ 0.5, find (ƒ˜¹)'(7) = dy y=7

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Q: For the function f(x) - 2r + 3z - ka + 2, where f passes through the point (1, – 2), what is the…

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Q: + The f(x) = Vx – 2 defined at (-0,2] T F

A: Given: fx=x-2 A real valued function is said to be defined in an interval I, if fx∈ℝ, ∀x∈I. Now if…

Q: for f(x)=2x4-5x3+7 find all potential points of inflection and map the intervals where the function…

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Q: For the function y = f(x) = x² – 2x, x x ≥ 1, find (ƒ-¹) '(3) = df-1 dy y=3

A: We have to find the f-1'(3).

Q: of af For the function f(x.y)= 7x-9y- 3, find and dy

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Q: Why is ƒ not a function from R to R if f(x)= ½? b. f(x)= Jx ? c. f(x)=±/(x² +1)? а.

A: Why is f not a function from R to R if,  a) f(x)=1xb) f(x)=xc) f(x)=±x2+1

Q: Given the function, f(x) = √x + x, use linearization at x = 4, to approximate f(4.1)

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Q: - Find F-T: for the functions -at e t70 1at tco e

A: We have to use integral formula.

Q: For the function f(x)=e5x+e−x defined on the interval(−∞,1], find all intervals where the function…

A: Find all the intervals for where the function is increasing and decreasing

Q: For the function f(x,y,z) = 1 + 2xy¹ − 325, find fx, fy, and f₂.

A: Given query is to find indicated partial derivative.

Q: For the following exercises, use the second derivative test to identify any critical points and…

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Q: For the function y = f(x) = -3x^3+8: Find df^−1/dy at y = f(5). (f−1)'(f(5))=

A: Solution:- first find the inverse of the function

Q: For the function f(x.y.z) = 1+ xy° - 4z*, find f f, and f.

A: We can find the partial derivative in the following steps.

Q: Describe the long run behavior of f(t) = - (t + 3)°(t + 1)(t + 2) As t → - 0, f(t) –→ ? As t → 0,…

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Q: Find the critical points of the function. 4 f(x,y) = 5+76xy +38x² +240y + 4

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Q: For the function f(x,y.z) = 3 + 4xy - 5z*, find f,, f, and f,.

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Q: For the function f(x,y) = -6x² + 4xy – 6y + 8x + 8y + 5, find and classify all critical points.

A: we have to find and classify all critical points

Q: Use the chain rule to find the derivative of f(æ) = 4(92". – 8a")" You do not need to expand out…

A: Given the function f(x)

Q: For the function f(x,y) = 5x² + 6y², find f(x + h,y)-f(x,y) h 11 f(x + h,y)-f(x,y) h

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Q: For the function f(x)= 3x² +2x–1, Find the equation of the line tangent to the curve at x = -1 2.

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Q: 3 f(x) = x2, with 0 < x < 1

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Q: a. by using the appropriate Chain Rule and b. by converting w to a function of t before…

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Q: Let f(x) = x² – 4x – 5, x > 2. Find the value of df-1/dx at the point x = 0 = f(5).

A: (f-1(x))' = df-1dx = 1f'(f-1(x))

Q: For the following exercises, use the second derivative test to identify any critical points and…

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Q: For the given function f(x,y)=x²y³+3x³y, find a flay

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Q: For the function y = x² + 2x, the value of dy when x=3 and dx=0.1 is (А) 0.15 B - 0.8 -0.15 D 0.8

A: The given function y=x2+2x  ;  x=3 and dx=0.1

Q: For each of the following exercises, a. decompose each function in the form y = f(u) and u = g(x),…

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Q: For the function y = f(x) = 5x -8: %3D df at x = -2. dx a. Find f'(- 2) = 52

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Q: For the function y=f(x)= x2+2x+4 x≥ −1 find df-1/dy y=12 (f-1)'(12)

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Q: For each of the following exercises, decompose each function in the form y=f(u) and u=g(x), and…

A: (1) Consider the function y and determine y = f(u) and u = g(x). y=x7+7x7Let u=x7+7xy=fu=x7+7x7So,…

Q: -at f(t) = 5e"t – 5e

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Q: For the function y=inx, find f(e^2)

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Q: (b) Find the Linearization of the function: f(x)= Vx at a= 27 and use it to approximate the number…

A: Let the function is f(x)=x3 Let a = 27   Formula: Linearization of the function f(x) at x = a…

Q: y2 For function f (x, y) = x2+1

A: