for the function f(x) = 2 cos(45x)o , determine:  the average rate of change for the interval 13  ≤ x ≤ 21.

Q: Find the derivative with respect to t for the function y = 2/t.

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Q: ind the derivative of the function f(z) = (2r+7) 71+11 %3|

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Q: Find the value of the derivative y′(x) at x=0 for the function given by ey+xy=e.

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Q: What is the closest value to the instantaneous rate of change of the following function at x = T?…

A: Ans:  Given  fx=2 cosx-π2  at  x=π          ⇒fx=2cosx coπ2+ sinπ2         ⇒fx=2cosx 0+sinx1…

Q: 0 to x = 5 Determine the average rate of change of the function y = sinx from x =

A:

Q: Let f '(x) = sinx - cos x. Where does the relative extremum value of occur? (a). 플 (b). (d). 프 (c).

A:

Q: 2. Compute the second derivative, f"(x), of the function f(x) = e*. %3D

A:

Q: 7n Find the average rate of change of f from t to 2 f(x) = cos 2 %3D

A: The average rate of change of the function is:

Q: Eョ2 T -(X子 ノ = (X)J fi(3)

A:

Q: Find the derivative

A: The first derivative of f(x) is represented byf'(x) and the second derivative is represented by…

Q: ind the rate of change to total revenue (in dollars) with respect to time when x = 10 and given that…

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Q: Use the second derivative test to find the local extrema for the function f(x,y) = x² +y³ + 2xy – 3x…

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Q: for the function f(x) = 2 cos(45x)o , determine: the instantaneous rate of change at x = 12. you…

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Q: The average rate of change of f(x) = sin(x) with respect to x as a changes from 0.5 to 1 is O 1 0 2…

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Q: Two students are calculating the instantaneous rate of change of y= sin(x) at x = Student A claims…

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Q: Find the second derivative of F(t) = | sin(x) cos(2)d.r.

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Q: (b) Find and simplify the derivative of the function pln(z) e dt. f(x) = |

A: we need to find the derivative of given definite integral

Q: ) Given the following derivative function 2x – 5 f'(r) = Þ – I^ what are the critical numbers of…

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Q: Let f(x) = derivative f'(x) equals o. e. Find the value of x for which the second

A: Given that: f(x)=32x2-ex

Q: Given f(x) = x^5 * cos x, dx= 0.01, use numerical differentiation to find: (1) df/dx for this…

A: Concept: The formula for the differentiation of the product of two function Let the two functions be…

Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

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Q: Use the h → 0 definition of the derivative to find f'(0) for f(x) I+1

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Q: Evaluate the derivative of the function r(t)=⟨sin2t,cost,2sect⟩ at t=π6.

A: To find the derivative of the given function.

Q: Find the approximate value of second derivative f"(0) with the step h for the following function by…

A:

Q: Find- for the following function dx x=a(cost + t sint).y=a (sint-tcost)

A: y=a(sint-tcost), x=a(cost+tsint) To find dy/dx.

Q: If f'(x) = 5x*, what is f(x)? (Use C for the constant of integration.) f(x) =

A: To find the integration

Q: Find the second derivative f"(x) for f(r) = e(z+2)*.

A: Given: fx=ex+24 for finding second derivative of given function we first take log and find first…

Q: 2x Using the definition of derivative, find Given y = dy %3D x+8 dx

A: dy/dx from definition of derivative is given below

Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

A:

Q: The height of an arch above the ground is given by the function y = 11 sin x for 0sxSr. What is the…

A: This question can be solved by applying the formula of average height of an arch.

Q: Find the slope and the rate of change of the slope with respect to x when t = 90°. x = 2 cos (3t)-3…

A: This question can be solved using the concept of first and second order derivatives at t=90°

Q: The derivative of the function y = cos -1 = COS Va at 1 is equal to 4 :Select one -2 .a V3 .b V3 .C…

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Q: The derivative of the function y = sin VE at a = is equal to %3D 4 14

A:

Q: Find the derivative dv/dpsi of v(x) V()| V(vi) where V(y) = (1 - e-√2 and 16 V (vi) = (1 - e-√2…

A: Given v(ψ)=VψVψi           (1) where Vψ=1-e-16π3ψ2 and Vψi=1-e-16π3ψi2 Since ψi≠ψ and ψi is the…

Q: Find the average rate of change (AROC) of the following functions over the interval [60 ≤x≤180] y =…

A: using , average rate of change…

Q: Use the implicit differentiation to find dy/dx for (e^x)y + tan(xy) - 5 = 0

A: Given that        (ex)y + tan(xy) - 5 = 0

Q: 3) Find the slope of the curve defined by f (x) = x° sin x at x = T. 4) Differentiate g(x) = e* .

A: The slope of a curve y=f(x)  at a given point x=a is the value of dydx  at the given point x=a. So…

Q: The height of an arch above theground is given by the function y = 10 sin x, for 0 ≤x ≤∏.What is the…

A: The height of an arch above the ground is given by the function y = 10 sin x, for 0 ≤x ≤∏.What is…

Q: Find a function whose 2nd antiderivative is f(x) = tan(x) + 4x+1

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Q: Find the second of the finchion, ç x) = cos e derivative f (x) (x %3D %3D

A: Consider the given function: f(x)=xcosx The first derivative is calculated using the product rule.…

Q: 8x Find the average rate of change of f from 0 to 3 f(x) = sin

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Q: S() dt, where f is a continuous function, find f(4). (c) A 10 ft ladder rests against a vertical…

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Q: 4) /() =2-2 3. 5) y = x*+2x+1 6.) f(x) =

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Q: for f(x, y) = sin(O 2- Find the third derivative for

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Q: Calculate the error of approximation with Ea for the following functions when x = 2, Ax = dx = 0.08

A: If the input of a function y=f(x) changes, its output also changes. The derivative of a function is…

Q: Show that, for a function f(x) with anti-derivative F(x), d s)ds f(x). %3D dx a

A: Suppose f(x) has an anti-derivate F(x), v(x) and u(x) are differentiable, then Leibniz's rule of…

Q: Integrate the following functions f(x)=Ln [sec (x)] [², 3]

A: We will see the graph of secx to judge the value of greatest integer function of secx.

Q: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

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Q: Find the length of the curve y = ln x from x = 1 to x = e.

A: Given:Find the length of the curve y = ln x from x = 1 to x = e.