For the following function f, find the antiderivative F that satisfies the given condition. f(x) = 8x° +9 sin x, F(0) = 7 The antiderivative that satisfies the given condition is F(x) =I.

Q: 3. For the function f(r) = cos(x) find V}(0,27).

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Q: For the function f(x.y.z) = sin'(5xyz), find fy. fy. and f (Type an exact answer, using radicals as…

A: f(x,y,z) = sin-(5xyz) fx = derivative with respect to x fx = 5yz/1-25x2y2z2 fy = 5xz/1-25x2y2z2 fz =…

Q: The coefficient of Sin(x) in the antiderivative of F(x) =| cos is 17/16

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Q: / f(x) dx, where Evaluate S822, f(x) = 9 sin(x), -T<x < 0 0 < x < T. f(x) dæ =

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Q: h(x) = sin² x + cos x О<x< 2л

A: We have to find the functional value at where either function is not differentiable or derivative…

Q: For the following function f, find the antiderivative F that satisfies the given condition. f(x) =…

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Q: For the following function ƒ, find the antiderivative F that satisfies the given condition. ƒ(x) =…

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Q: Find the general antiderivative of f and check your answer by differentiating.  f (x) = 2 cos x − 9…

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Q: Given that f"(x) = cos(x), f'(T/2) = 2 and f(T/2) = 12 find: %3D - f'(x) = f(x) =

A: Given: f''(x)=cosx

Q: For the following exercises, find the linear approximation L(x) to y = f(x) near x=a for the…

A: Consider the following function: fx=sinxf0=sin0=0 Differentiate fx with respect to x:…

Q: Given t2 – 1 dt 1 + cos²(t) At what value of x does the local max of f(x) occur? f(x): %3D

A: Part 1 of the Fundamental Theorem of Calculus : If  f(x) = ∫axg(t) dt then  f'(x)= g(x)

Q: For f(x, y) = sin(9xy) evaluate fz at the point (2, 4

A: Answer is mentioned below

Q: Find the general antiderivative of f and check your answer by differentiating:   f (x) = 4x7 − 3 cos…

A: Given: fx=4x7-3cosx

Q: Find the general antiderivative of f and check your answer by differentiating:   f (x) = ex − 4 sin…

A: Find the general antiderivative of f and check your answer by differentiating:   f (x) = ex − 4 sin…

Q: Let f(x)= sin(x) – e¯*, po=0, and p,=1, then by Secant method p2=

A: f(x) = sin(x) -e-x  p0 = 0 and p1= 1

Q: Find a and b which make the following function differentiable at x = 0; ax+b, x < 0 sin x, f(x) = =…

A: We know a function is differentiable if and only if Right hand derivative and left hand derivative…

Q: Find the most general antiderivative of the following functions. (d).r(θ) = (sec θ − tan θ)^2

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Q: 5. Given a piecewise function sin t, 0st< f(t) = {0, (t, i. Express f(t) in the form of unit step…

A: Given: (i) To express f(t) in form of unit step function (ii) To find L{f(t)}

Q: Given f(2) = , 1+ cos (t) = |. t2 – 16 dt 1+ cos²(t) f(x) : %3D At what value of x does the local…

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Q: Find antiderivative of the following functions.  1. f(x)=sinx/(1+cos2x)  2. f(x)=x/(1+x4)

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Q: Find f. (Use C for the constant of the first antiderivative, D for the constant of the second…

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Q: 3. If f(x) = cos(x), determine f(125) (-T). V2 (B) 2 (A) 0 (С) 1 (D) –1 1 (E)

A: we will use nth derivative formula of cosx .

Q: Find the most general antiderivative of each of the following functions  f(x) = sin x

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Q: Find the general antiderivative of the given function. f(x)= sin (7y)+ cos (3y)

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Q: For the given function f(x) = cosx, let xo = 0, %3D X1 = 0.5, and x2 = 0.7. Find the value of…

A: From the given x=0.75, x0=0, x1=0.5 and x2=0.7. It is known that, the lagrange interplotation…

Q: Find f. (Use C for the constant of the first antiderivative, D for the consta f"'(t) = Vt - 3 cos(t)…

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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: Given y=-6sin-3x To decompose the function in the form y=f(u) and u=g(x) Here    y=-6sinx-3 u have…

Q: Find that antiderivative of the function whose value t2 + 2t + 2 IT tan- (t + 1) + 1 – 4 None of…

A: we have to solve intigration

Q: For the following function ds find the antiderivative s that satisfies the given condition. dt ds -=…

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Q: Apply the chain rule to differentiate the following functions. Show your complete solutions and…

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question. If…

Q: Now evaluate f(x) for x = 4n. 47 f(4t) = sin 4 Therefore, the possible point of inflection is as…

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Q: Find the general antiderivative of each of the following functions. h(x) = sin 2x

A: Given:                  h(x)=sin2x   To determine:                  The general anti-derivative=?…

Q: Given that f(x) = sin a cos' r +2 (sin r + a)' +, the value of the constant and the least value of f…

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Q: In solving the antiderivative of f(x)= 3sin(x) + 4cos(x) +5 by miscellaneous substitution, the…

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Q: For the following function ƒ, find the antiderivative F that satisfies the given condition. ƒ(ν) =…

A: For  find the anti derivative of function f(x):Let f(x)=ax+b Integrate the function both side…

Q: Find all values of the constants m and b for which the function S sin x, y : тx + b, х 2п is a.…

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Q: For the following function f, find the antiderivative F that satisfies the given condition. f(x) =…

A: For the following function f , find the antiderivative F that satisfies the given condition.  f(x) =…

Q: The function f : XI→ a + b cos x, is defined for 0 sxs 2n. Given that f(0) = 10 and that f (n) = 1 ,…

A: The range of a function is the values that can be obtained from the function by substituting all the…

Q: For sin y=- find the value of so that (y+y")= - 1 at 1 at x=0 Cos X-

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Q: a² f For the function ƒ(x,y), compute Or d0 if x =r cos O and x=r sin 0 .

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Q: For the following function 1, find the antiderivative F that satisfies the given condition. f(x) =…

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Q: For the following function f, find the antiderivative F that satisfies the given condition. f(x) =…

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Q: For the following exercises, find the linear approximation L(x) to y = f(x) near x=a for the…

A: fx=sinx, a=π2 The linear approximation of a function y = f(x) at x = a is Lx=fa+f/a·x-a Now…

Q: For the following exercises, find the linear approximation L(x) to y = f (x) near x = a for the…

A: Consider the given function: fx=sin2x ,a=0 Here, the objective is to find the linear approximation…

Q: Find an antiderivative F(x) of the function f(x) = 5 sin(x) such that F = 3. F(x) Now, find a…

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Q: For the following function f, find the antiderivative F that satisfies the given condition. 3 f(x) =…

A: Here we have to find the integral of the given function with given condition.

Q: Given x² + 13x + • 40 f(t) = 1+ cos2(x) At what value of t does the local max of f(t) occur? rp- t =

A: Here, the given function is: f(t)=∫0tx2+13x+401+cos2xdx

Q: For the following exercises, find the linear approximation L(x) to y = f (x) near x = a for the…

A: Express the linear approximation of a function f(x) at x=a. f(x)≈f(a)+f'(a)(x-a) Given that,…