L{e' f(t) + g(t)} = f (t) (S-1)4 . From the options below choose the correct expressions for and g(t). O O f(t) = sinh (3t), g(1) = 3t f(t) = tª, g(t) = 31313 f(t) = t³, g(t) = sin (31) + f(t) = e³¹, g(t) = cos (31) 3 (s² + 9)

Q: 8. Find the function Sthat satisfies the given conditions. )S"(=) = sin r – e-2" with S"(0) = } and…

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Q: An object moves along the x-axis with velocity given by v(t) cos(t) m/s || Suppose that the object's…

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Q: Four equations are provided below. Which equation follows from the Power Rule? I. (P)' = pr P 1…

A: Answer is option (a)  Because only equation 3rd follows the power rule .

Q: 2x2sinh(x3)cosh?(x3) Option 3 O :The dy/dx for the y(x) = sinh?(x3) cosh ²(3x²) Option 1 O 6x2…

A: Solve for the given

Q: tan z, find v(/6), (z – ), V(-z), and express (2z) as a 9. If v(z) function of (z).

A: As per the guidelines when multiple question are posted in single pic  then we are supposed to solve…

Q: 13x Find the derivative of the function y = 2 tan¬1 (5x ). (Use symbolic notation and fractions…

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Q: f f(x)=sinx and f(x)=-1, calculate x for 0°<x <360°.

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Q: V3 sin- (x) dx V1 – x² 0.

A: Here we have to find the given definite integral value.

Q: X(t) = b cos(wt) + V a² – b² sin²(wt)

A: We will use differentiation rules to solve this question.

Q: Answer the following questions for the function f(x) = - 8x°- 36x +240x - 11. a. Find formulas for…

A: derivative

Q: 2. 1 Evaluate the definite integrals below. Use u-substitution when appropriate. 4 5 3el/x (a) (b) |…

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Q: f(x) =-3 sin 3. Determine the amplitude, period and phase shift of the graph of f(x) for - 2r sxs…

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Q: Identify the function f (x). I (x) = (f (x))° = cos 2x

A: Given,          lx=fx6=cos62x

Q: Q:Findthe domain of the following functions sin 'x (1) s''x (i) [x] 1 (ii)- | x | ,× cos 'x

A: In this question, we need to find the domain of the given functions.

Q: The derivative F' (t) is graphed in the figure below. Given that F (0) = 12, calculate F(t) for t =…

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Q: r' (t) × r´ (t) to ||r' (1) × r´ (1)|| Use the formula B (1) = T (1) × N (t) to find B (t) , and…

A: Given that rt=sint-tcosti+cost+tsintj+48k. To find Binormal vector B(t).

Q: Find y as a function of t if y(0) = 8, y'(0) = 3. y = 64y" + 304y +361y = 0,

A:

Q: 8x Given f(x)=x-1 and g(x)= x? -1 8x Show that y = f(x)· g(x)=- x+1 i) ii) From your answer at (i),…

A: Given: f(x)=x-1 and g(x)=8xx2-1.

Q: Solve the initial value problem below using the method of Laplace transforms. y" - 4y' - 12y = 0,…

A: Given equation is: y"-4y'-12y=0 ,y(0)=1,y'(0)=38 We have to find the value of y(x)

Q: Consider the function f(x) = 3 sin (r). Find the equation of the line tangent to the curve f(x) = 3…

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Q: . Consider f(x) = 4 - x2 , g(x) = Vx + 3, h(x) =. Evaluate the following. %3D 1. (f° g)(1) 2. (g•…

A: Explanation of the answer is as follows

Q: 27: let f(x) = tan(x)+ sec(x) find f"(x)

A: As per our guidelines, we are allowed to answer only one question. Since you have asked multiple…

Q: 3. Find the derivative y(15)of the function y = (x2 + x)sin(2x).

A:

Q: 4. Prove that cos(sin¬1 x) = /1 – x².

A: cos(sin-1x)=1-x2⇒sin-1x=cos-1(1-x2)Let y=sin-1x                               (1) ⇒siny=x…

Q: A2) Find the derivative of the following functions 1² + 3 z² – 3 (a). f(x) : (b). f(x) = 2 tan (x) –…

A: As per bartleby guidelines, we are supposed to solve only first three subparts if multiple subparts…

Q: Find the derivative of 7 (t) = (1+t°, te¯t, sin (2t)) A. F'(t) = (3t°, (1 + t)e¯t, 2 cos (2t)) B.…

A: We are asked to find the derivatives.

Q: Find f. f'(t) = sec(t)(sec(t) + tan(t)), = -1 2 (t) = tan(t) + sec(t) – 1- V2

A:

Q: show that the inverse of arotation matrix is transpose,which is also arotation matrix, and it is…

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