Q: Show that the following functions are inverse functions? 1. Vãy = x2- 4x + 16V , x24 x-2 2. y = (2-x)2 Q: Answer one only: - A- If y = e3* and y = e-3*, prove that: - d'y d - 9y = 0 B- If y = cos*x - sin*x, prove that: - d'y = -4cos2x dx Q:: Find for the following functions: - xp b- y = x*. e-2x, cos5x a- y = (cosx)v (use logarithm differential) C- csc/3V5x

Q: (a) Is Rolle's Theorem applies for the function ƒ(x) = cos(sin¬'x) on the closed interval [-1, 1]?…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the iterative scheme for the root of equation cos x- 3x+1=0 by Newton-Raphson method. O a. None…

A: Newton rephson method problem....

Q: Consider the function f(x) = cos x - 3x + 1. Since f(0)ƒ () <0. f(x) has a root in [0]. If we use…

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Q: 17. Derive A) f(x) = 10x* –- 32x + e² %3D B) y = e-* sin x

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Q: Determine ƒ such that (1, sin 1) is on the graph of f and e2z + 5e² + sin æ ifx 0

A: When derivative function is given, to find the actual function integrate the given derivative of the…

Q: Differentiate the following functions. Show your complete solution and box your final answers. x5/2…

A: As part guideline we have to solve three subparts

Q: (a) Is Rolle's Theorem applies for the function f (x) = cos(sin-1x) on the closed interval [-1,1]?…

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Q: dr 1- y = Inlog 2- y = (cos x)*Snx 3- у e (sinx

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Q: Determine if f is differentiable at x = 0 given that -1 4 cos if – 2 0, x # 1. (x – 1)6 '

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Q: Find if f(x, y) = x2 +2xy cos x .

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Q: 29. A water ride with heights above and below the starting point can be modeled by the function y =…

A: Given: The function of height of water ride varying with time as y=3sinπ2x+3-2, where 0&lt;x&lt;5.…

Q: dy Find as a function of x when y = sin°(x) %3D O 1) 5cos (x) 2) 5sin (x)cos(x) 3) 5sin (x) 4) 5cos…

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Q: 9. 10. If f(x)=√ex, the derivative is: √ex a) f'(x) = Vex b) f'(x) = √ex c) f'(x) = 2x Which of the…

A: Calculate the derivative of both problem in the following way:

Q: Q5: Find for the following functions: (1) In(x - y) = xy + y³; (4) y = x sinh 2x-cosh 2x (2) y =…

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Q: Q5: Find for the following functions: (1) In(x - y) = xy + y³ (2)y=tan³ √/cot(7x); (4) y = x sinh…

A: Solution is given below:

Q: 7. If aatiß = (x + iyy*4, a>0, prove that %3D (i) a = 5 log, (x + y) -q tan log, e- loga (r + y) =…

A: The given isaα+iβ=x+iyp+iq,a&gt;0.prove thati α=12logax+y-qtan-1yxlogaeii logax2+y2=2αp+βqp2+q2

Q: Using the substitution t = tan(), the integral 2 dx sin(x) – 78 cos(x) can be written as dt 39 – t-…

A: To make substitution and re write the given Integral.

Q: Determine f such that (1, sin 1) is on the graph of f and e2z + 5e² + sin x ifæ 0

A: Given f'x=e2x+5ex6ex+sinx    if x&lt;01                           if x=0x5x2+1+cosx if x&gt;0 We…

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () < 0, f(x) has a root in [o,]. If we use…

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Q: Differentiate the function: y = e-x cos²x x²+x+1

A: To differentiate the function.

Q: dy using either version of dr (1) First, identify the inner and outer functions. Second, determine…

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Q: 1. Use implicit differentiation to find if y? = x*siny. 2. Find the value of given the equation 6x³…

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Q: •5 6- Let f(x)dx = 10, f(x)dx = 9, f f(x)dx = 2. Find f(x)dx and (10f(x) – 9)dx =

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Q: by implicit di f foretiation of sin-(xy) - cos-(x- y) Find -V1- (xy)? xV1-(x- y) ² + V1- (xy)? -V1-…

A: Using Implicit Differentiation

Q: 1. Evaluate f sin*(2x + 3)cos (2x + 3) dx sin(2x + 3) put = t 2. Evaluate f dx Put x2 + 5 = t x2+5…

A: Explanation of the solution is given below.....

Q: Thus, for u = g(x) = sin(5x), %3! f'(g(x)) = F'(sin(5x)) = 8 %3D %3D 8 Next we calculate g'(x). g(x)…

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Q: 2 Given that: J2(x)=-, cos.x + sinx find J(x)

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Q: 1. Find for the following functions : dx 4i) y-bmcx* +2y}kos x (ans.: 4x.cos x - 2 In( x² + 2 )sin x…

A: To find the dy/dx of  y=[ln(x²+2)²]cosx

Q: 4. The given equation sinh(xyz) = x + y + 3z implicitly defines a differen- az tiable z as a…

A: Differentiate with respect to x keeping y as a constant.

Q: Consider the function f(x) = cos x -3x+1. Since f (0)f () <0, f(x) has a root in [o]. If we use…

A: Given that                     f(x)=cos x-3x+1 Newton-Raphson iteration scheme is…

Q: cos(3x) if x 1 if x = 0 or x = 1 3* if Let f(x) = 3 + In x if 3 Then f has removable discontinuity…

A: We will solve the following

Q: 1-Let :=x+iy then cosh(iz ) is equal to a-cos' y+ sinh' x b-cosh' y-sin'x e- sin' x+ sinh v d- None…

A: Let z=x+iy therefore, iz=ix+i2y=ix-y=-y+ix we know that  coshz=ez+e-z2 therefore, cosh…

Q: 5. (a) Find all functions y = f(x) satisfying dy/dx = sin(2x) + x. (b) Find the one function from…

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Q: 7. Differentiate the following functions. sec (x³+1) b. у 3 cos yx

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Q: 1 dt, where g(x) cos x If f(x) = g(x) [1 + sin(t²)] dt, find f'(7/2) %3D /1 + 8 Select one: 21 sin…

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Q: Can you help me with this problem step by step?

A: The given expression is,

Q: 1 Find that antiderivative of the function whose value at X = –1 is x2 + 4x + 5 0. x + 1 In |x+5 -…

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Q: 1 = cos t and f(0) = 4 f(0) + f(0+ 2T) + f(0+ 47) ? If f(t) = cos t what is the exact value of %3D 3…

A: ft=cos t and fθ=-14

Q: Indicate if the following function increase or decrease at given interval: f(x) = 3x² + 2 cos(x), х€…

A: Check the each function by first derivative test. In the given interval if the derivative is…

Q: 15. Determine if the given functions are linearly dependent or independent. (Prove your answers) {e…

A: 15.  a) Given, e2x, 3x Now the Wronskian is, Wf, g=fxgxf'xg'x=e2x3x2e2x3=3e2x-6xe2x≠0 Since the…

Q: If it was f(x,y)=y cos(6xy) SO a² f Əy² 2² f Əy² a² f Əy² a² f Əy² = 36 x²y cos(6xy) + 12x sin(6xy)…

A: A detailed solution is given below.

Q: Consider the function f(x) = cos x - 3x +1. Since f(0)ƒ () <0, f(x) has a root in [0]. If we use…

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Q: Consider the function f(x) = cos x − 3x + 1. Since f (0)ƒ () <0, f(x) has a root in [o,]. If we use…

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Q: Find f(4) if Jo f(t) dt = x cos Tx.

A: Here given as ∫0xftdt=x cos πx Difeerentiate with respect to x ddx∫0xftdt=ddxx cos πxfx=xddxcos…

Q: 2. Consider finding the root of f(x) = e"(3.2 sin(x) - 0.5 cos(x)) on the interval [3, 4], this time…

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Q: Express Q (x) = cos* (x² + 1) as the composition of three functions. That is, identify f, g, and h…

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Q: If f(2, y) = 3 sin(2x +y) - 4 cos(z- y) then the second derivative f is %3D a. -12 sin (2x +y) +4…

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Q: Evaluate D°(cos x+e-2*) (A - cos x +64e -2x B - sin x – 32e -2 cos x – 32e-2 D sin x +64e -2x

A: Explained below