2? sin ? a +0 x = 0 Let f(x) = (c) Show that f'is not continuous at x = 0.

Q: dy Use implicit differentiation to find given dr tan(x + 2y) + cos y = x² – y²

A: From the given problem;   tanx+2y+cosy=x2-y2   Now differentiating with respect to x.…

Q: 2. Express in indicated derivative in terms of the function F(r). Assume that F is differentiable.…

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Q: What are all absolute and relative extreme values of the function f(x)=– sin z on the interval (0,…

A: Given function f(x) - f(x) = -sinxDifferentiating on both sides with respect to x - f'(x) =…

Q: What is the indefinite integral (anti-derivative) { cos(x) dx? ○ sin(x) + C cos(x) + C - sin(x) + C…

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Q: sec?x Integral tanx

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Q: (sin(x)²) dx Is it converges?

A: Given integral is ∫0∞sin(x)2xdx firstly we will find the simplest form of integration. We have…

Q: differentiate the funtion y = cosh x - sinh x / cosh x + sinh x

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Q: Evaluate the indefinite integral: ∫sec x tan x dx

A: Given indefinite integral is ∫secxtanxdx

Q: What is the derivative of cosh-1(xy) + elog x = sec3(y2)

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Q: Use the definition of a derivative to find f' (0) where: x² sin(÷) x+0 x = 0 f(x) = f the derivative…

A: Given function is f(x)=x2sin1x0,     x=0,x≠0 By definition, f'(0)=limx→0f(x)-f(0)x-0

Q: Use substitution to evaluate the indefinite integral. sin x cOS x dx sin x COS X dx =

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Q: / f'(x) sin x dx = 8, / f(x) cos x dx?

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Q: Let f:[-n, 7] –→ R, where f(x) = 2 sin (2x) – 1. TC Calculate the average rate of change of f…

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Q: Find the average rate of change of f from 0 toπ/2 . f(x)=sin( x/2)

A: Derivative of a function determines the change of one variable with respect to another variable.…

Q: Find the derivative. y = sinh 1(tan x) O y = |cos x| O y = 1 /1+tan x O y = 1 Vtan? x-1 O y = |sec…

A: In this we have to find integration and derivative.

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: Determine whether f(x) is differentiable at x = 0. Show your work. sin(x) cos(x)-1 3x + 1 f(x): = if…

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Q: What is the derivative of f(x) =2cos (x)? %3D 2 cos (2x) O -2 cos (2x) O 2 sin (2x) -2 sin (2x)

A: f(x) =2cos2xdifferentiating w.r.t xd(f(x))dx=ddx(2cos2x)

Q: Evaluate the indefinite integral.

A: Consider the given integral I=∫sec3x·tanx dx

Q: Q: Show that the function f(x)=- x sin ,X =0 is continuous at x = 0.

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Q: Given x sin (yz) + y³ cos (xz) + z sin (xy) = v3. Find (a) implicit differentiation (b) by partial…

A: 1st we will use implicit differentiation with chain rule and for next part total derivative

Q: (ups" = (In tanx) (x*) ( Sinx) (Ny)" sec"('s %3D 2. %3D

A: Here we apply logarithmic differentiation for both Questions

Q: Use the Second Derivative Test to find all relative extrema. (a) h (x) = x - 2 cos x, [0, 4π]

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Q: Evaluate sin(x) · In ( cos(x)) dx using integration by parts.

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Q: dy Use implicit differentiation to find ɖ& er + x - ỷ = 10 1) f(х) - Зе* - 8еsx %3D 2) Find the…

A: Sum Rule of differentiation : ddxax+b=ddxax+ddxb Chain Rule of differentiation : ddxfgx=f'gx×g'x…

Q: (a) Evaluate the indefinite integral (anti-derivative) x°(1+ 2*)® dx by using the substitution u =…

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Q: :Show that the function 1 x sin When x + 0 S(x) =- 0, is continuous but not differentiable at x = 0.…

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Q: derivative of y with respect to x. y= In (6 In x) dy dx %3D

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Q: dy Using implicit differentiation find at the point (0,1) for dx ysinx + xy3 = 5

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Q: Evaluate the integral. π f(x) dx   0   where    f(x) =    sin(x)    if  0 ≤ x <  π 2 cos(x)    if…

A: we need to evaluate the integral of πf(x).dx given that  f(x)=sinx if 0≤x≤π/2       cosx if π/2 ≤x…

Q: What is the second derivative of y + Incosx = 0 * O (cos x) ^2 O 1 O (sec x)^2 tan x

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Q: Find a nonzero value for the constant k that makes th tan(kx) x 0 Continuous at x = 0.

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Q: Differentiate the function. f(x) = sin(x) In(3x) sin (x) f '(x) + cos (x) In (3x)

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Q: 5) Use the Fundamental Theorem of Calculus to define of the function fol=sin (x?+!) ant-derivative…

A: According to the fundamental theorem of calculus, the following expression is to be true if F is the…

Q: Prove dx dx 1 f ( sec -x+tan –I 2 1 | f (cosecz) %3D Vsin r sin x

A: Apply trigonometric properties to prove the result.

Q: Find the linearization of ƒ(x) = sqrt(x + 1) + sin x at x = 0. How is it related to the individual…

A: To determine the linearization of the function at x=0.

Q: dy Use implicit differentiation to find dx x sin (5x + 6y) =y cos x

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Q: Find a positive value for the constant "u" that makes tan Sur x<0 f(x) = continuous at x= 0. 2x +…

A: Given:               fx=tan5μxxx&lt;02x+2k3x≥0

Q: Find the indefinite integral C sec x tan x +3 sec x) dx.

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Q: Use Dnf (x) to approximate the derivative of f(x) = sin(x) at ;h = (0.01,0.2) 4

A: Given fx=sinx at π4, h=0.01,0.2

Q: find the most general ntiderivative f(x) = 4 sec2(x) + 3 sec x tan x

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Q: Find the indefinite integral. ∫sec x tan x/ (sec x − 1) dx

A: Given:∫secx tanxsecx-1 dx

Q: B) Prove that: cosh (x + y) = coshx coshy + sinhx sinhy %3D

A: We know that cosh(θ) = eθ+e-θ2sinh(θ) = eθ-e-θ2

Q: Show that is zero in two differentiation steps only. f(x,y) = xe*/«_ %3D Show that is zero in three…

A: Consider the provided question, According to you we have to solve only (7) - part (b) and (c). (7)…

Q: Which of these is the derivative of y = sinh x ? - sech x tanh x - cosh x csch x sech x -csch x…

A: To select the option for the derivative of,  y = sinh x

Q: 6. Is f continuous at 0? Explain your work carefully. { 2² . sin(-) + cos(-) ifz+0 | f(x) = %3D if x…

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Q: limit x approaches zero, sin^2x/x

A: Given,