(8) Giry thieo examplos of functions f=IR→ IR is not megasurable. -

Q: The equation of tangent line of the function 21 x3 f(x) = e7e dt %3D 21 x at x=1 is V21 e3087 (x-1)…

A: Given function is  f(x)=∫21x21x3e7t2dt Since at x=1, upper limit of the integral is equal to lower…

Q: Question 1 Find the total differential of the function z = 7x³y8 Odz = 7x¹y³dx + 7x³y+dy dz =…

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Q: Find the curve y(x) that minimizes the I Cy) = S. cos x)+ ]2 Cunc tonal %3D

A: solution:-Given I=∫1+cosx+y121/2using Euler's equation ∂f∂y-ddx∂f∂y'=0sincef=1+cosx+y121/2is…

Q: Prove the formula for the derivative of a) (Inverse of cotangent) b) (Hyperbolic cosecant) y = csch…

A: formula for derivative of both function is following:-

Q: Show that the function e (cos y +i sin y) is holomorphic (anal ytic) and findits derivative.

A: u(x,y)=e^x*cos(y) and v(x,y)=e^x*sin(y) We prove Cauchy Riemann satisfy everywhere

Q: Is there a smooth (continuously differentiable) curve y = ƒ(x) whose length over the interval 0 ≤x ≤…

A: Here it is required to find a curve.

Q: Find the value of the derivative (if it exists) at each indicated extremum.           f(x) = cos x/2

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Q: If the acceleration of a particle is given by ä = sint i+ cost +e k, find the relity and position…

A: The acceleration of a particle is…

Q: Where is the function f(r+iy) = 4y – 5ix differentiable? Where is it holomorphic? Determine it:…

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Q: 4) a²y=+52y =14 yat (2,1) Find equátion of tangent?

A: Equation of tangent  y-y1=m(x-x1) (x1,y1)are the points at which equation of tangent is to be…

Q: Show that the function y=| × | is differentiable on (-o,0) and (O, c0) but has no derivative at x =…

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Q: What is the equation of the tangent line to the function y = e-* – arcsin( 2 at x= 0 ? A) y - (1+) =…

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Q: 2. What is the largest possible area of a triangle with its base on the x-axis between x= 0 and…

A: The given curve is y=sinx. To find the largest possible area of the triangle with its base on the…

Q: I. Find an equation of the tangent line to the graph of t cosh (f² – 1) dt tan-l † | f(x)%3D /1+ln…

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Q: az Find dz by implicit differentiation, and confirm that the and dy results obtained agree with…

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Q: Is there a smooth (continuously differentiable) curve y f(x) whose length over the interval 0sxsa is…

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Q: Determine the equation of the tangent line to the graph of g(x) = mz [1 – sin(ne')]dt at the point…

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Q: Find the point where the CAUCHY- RIEMANN equation is satisied for the function f(2) =xy+Xyi

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Q: Determine the points in the interval (0, 2T) at which the graph of the function below has a…

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Q: 6.) y'of y = Insin(arctan 3x)

A: This is a basic differentiation question

Q: nd the points at which f(x) = cos² x has a horizontal tangent line. %3D

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Q: 5. As a particle moves through the first quadrant, its a and y coordinates are functions of time t,…

A: Given tan(theta)=y/x

Q: ion ƒ(x) is infinitely differentiable and that f'(x) = - st, second, third and n-th derivative of f…

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Q: what is of point Fyl-2,0) fexsy)=(x3ーy+g)s

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Q: Q-1: find the derivative of y with respect to the given indepe 1. y = In(Inx) 2. y = In(In(Inx)) x…

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Q: HG)- sinh 3x-1 Itcosh Vax1

A: Solution: Consider the given hyperbolic function is H(x) = sin h3x-11+cos h3x-1 Differentiating with…

Q: Find the absolute extrema of the function on the closed interval.                         y = 3 cos…

A: The given function is y=3cos x on 0,2. Compute the critical points on the given interval as follows.…

Q: 3/20 What is the equation of the tangent line to the function y = e*- arcsin) at x= 0 ? A) y- -(1+)=…

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Q: Suppose for sume function f we heve its derivative, f'cx) = e*sin(x), on the %3D interval o< x< ar.…

A: fx is a function such that f'x=exsinx on the interval 0&lt;x&lt;2π We have to determine where the…

Q: The derivative of the function y 1 = COS Va at a = 0 is equal to

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Q: 3) Consider the fonction (a) The tangent plare to the graph of fCx,y) at the point Co,0) is (b) At…

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Q: Find the derivative of the following functions: = Arccos 4x -4 ans. y' = V1-16x2 4. y = Arcsec(sec…

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

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Q: Find the equation of the tangent line to the graph of F(r)= 2z²+2r+1 evi dy at r 0. sech z

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Q: Find the derivative of the foll owing functions. Show complete solutrons, including trigonometrie…

A: As we know that; The Power law; ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x   And…

Q: A particle moves along the x-axis with acceleration given by 5T sin (at) for time t > 0. If the…

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Q: tanh" (cose 3x

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Q: The slope of the tangent line to the graph of y = ln x at x = a E R approaches infinity as a → 0+.

A: Given curve: y=ln x

Q: Determine the equation of the tangent line to the graph of g(x) = Sm, [1 – sin(ne')]dt at %3D In x…

A: We have to find the equation of the tangent line to the graph of gx=∫lnx01-sinπetdt at the point…

Q: +Inz 1. Determine the equation of the tangent line to the graph of f(r) = | V3 + 5t5 dt at x = 1.…

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Q: (a) If f(x.y) = e siny - e sinx then verify that fry fyz- %3D

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Q: The derivative of y = In(sin(ex + 1)) is O y' = -ex cot(ex + 1) the above y' = -ex tan(ex + 1)

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Q: 2. If the acceleration function of a certain particle is given by a(t) = sech () tanh (;) – ež, find…

A: If the acceleration of the function is a(t) then the velocity of the particle is obtained as…

Q: Find the values of x on [0, 2 ) π where the tangent line of f x( ) be horizontal. y=e^-x (cosx)

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Q: Suppose that the tangent line to the graph of y = f(x) at x = 2 is y = 4x – 3 and that the tangent…

A: The given tangent line to the graph of y=fx at x=2 is y=4x-3 and the another given tangent line to…

Q: 10. Compute the central difference approximations of O(h^4 ) for the first derivative of y =cos(x) +…

A: Solution is below

Q: The equation of the tangent line for the graph of Fx)= | Ln(P+4)dt at x=2 is F(x)=

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Q: 2. If the acceleration function of a certain particle is given by a(t) = sech () tanh () – ež, find…

A: The differentiation of velocity with respect to time is known as acceleration.

Q: Cualuate the definle integial. x33 COs (xH) dx

A: