Use the definition of continuous to proce whether or not the function is continuous at x=5z (F2, D3) Consider the function f(x) = Jx-5. Using the definition, find f'(x)

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Q: 75. F(x) : (t + 2) dt

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Q: . Differentiate the function using product rule. f(x) = e*(e* + sin x + x²)

A: Given : fx = exex+sinx+x2

Q: glay). ty sin Ctg) if مره( - إد x( %3D

A: Given that gx,y=x2+y2sinx2+y2    if x,y≠0,0a                     if x,y=0,0 To find the value of a…

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Q: Find the derivative dy/dx of f(x) using implicit differentiation. f(x) = sinx+cosy=sinxcosy

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Q: Use Linear Approximation to estimate Aƒ = f(3.02) – f(3) for f(x) = sin(). (Use decimal notation.…

A: Given: fx=sinπx16 We need to estimate ∆f=f3.02-f3 using Linear Approximation.

Q: The function f(x) is differentiable on (0, 1) and satisfies f(0) = f(1). However, its derivative is…

A: Consider the given function: Here the objective to check whether the given function contradicting…

Q: tion f defined as xy Ax, y)=- when (x, y)#(0, 0) when (x, y)=(0, 0) =0, is continuous at the origin.

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Q: Why is the function f(x)= cotx not differentiable on the interval [0, pi] ?

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Q: Assume that f : (0, 1) → R is a differentiable function with the derivative f' increasing on (0,…

A: Given f:0,1→R is a differentiable function and derivative of f is increasing in 0,1 that is f'x>0…

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

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Q: Prove the differentiation formula (d/dx)  [sech x] = −sech x tanh x

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Q: Using limit definition of derivative, prove d/dx e^x=e^x

A: We using limit definition

Q: Use the first derivative test to find the local extrema of the following function: f(x) = sin x –…

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

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Q: Where is the function defined by f(x) = In (x) increasing? Where is f(x) decreasing? Where is the…

A: Given a function: f(x)= ln(x) and the function is defined in the domain x∈(0, ∞)Then, f'(x)=1x

Q: State the Mean Value Theorem. Use it to show that for all x ≥ 0, 0 ≤ tan^−1 x ≤ x. [Hint: Use Dx…

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Q: Use Caushy Reman equations to Show that ĕ (Z) anel its derivative f(Z) exist Verywhere and find ぐ(z)…

A: Given: fz=z3 Rewriting given function we get, fz=x+iy3fz=x3-3xy2+i3x2y-y3 Now comparing, it with…

Q: 2. Using the definition of derivative, prove the following: (a) fo= if s)-V (b) y-sec'x if y tanx

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Q: Suppose f is differentiable with continuous derivative on [a, b]. Show that lim f(x) sin(nx) dr = 0.

A: To prove the given limit

Q: compute the derivative. f (z) = z tan z

A: The given function is f (z) = z tan z To compute: Derivative of  f (z) = z tan z

Q: Using the definition of derivative, prove the following: (a) f'(x) = 3Vx if f(x) = Vx (b) y=sec?x if…

A: (a)  fx=x13  Differentiating once f'x=ddx(x3)  f'x=13x13-1  f'x=13x23

Q: The derivative of the function Ve-tanh a is O y = -sech3x vetanh z 2 O y = -sech?x Ve-tanh / 2 O y =…

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Q: By using caushy Rieman find the derivative of f(z) =|z| if it exit O fiz) = 2 +I21

A: As per bartleby guidelines only 1 question can be answered please upload the questions separately.…

Q: Find the x-value of the extrema by using the Second Derivative Test. Justify your answer. f(x) =…

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Q: Show that the function f(z) = sin x cosh y + i cos x sinh y is continuous as well as analytic every…

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Q: HW prove That The derivative of Flx)=x-x is if (x) = 3x?1 use definition of devivativeto finid The…

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Q: Use integration by parts to prove the reductionformula.

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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 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: Use Linear Approximation to estimate Af = f(3.02) – f(3) for f(x) = sin(). (Use decimal notation.…

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Q: Find the derivative f(x) , f(x) = / sec (t) dt sec x -sec x tan x

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Q: 5 f(x) %D sin x

A: Given  f(x) = 5sin x We have to check the continuity of the function on the interval [0, 2π].

Q: Find a value of c that makes Continuous extension the function 9x - 3 sin 3x 5x f(x) = c, continuous…

A: The given function is

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: find the intergral of f(x) = sin(x) + cos(2x) on the interval [0,pi]

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Q: Differentiate by using implicit differentiation x2y+xy2=6

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Q: (a) (b) Explain the differentiability of f on R by using definition. Let f' be the first derivative…

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Q: Find the most general antiderivative. Verify with differentiation f(x)=cosx + 2sec^2x

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Q: Use fundamental theorem of calculus .4 –dx x In x 2,

A: Follow the steps.

Q: Find the range of f(x)= sin x+ vsin'x+sin'a cos x. COS X. %3D

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Q: Differentiate the function. y= (Sin x)In x

A: Given function - y = sinxlnx                   .............(1)Taking logarithm ln on both sides -…

Q: Show that the function f(z)=sin x coshy+I cosx sinh y  is continuous as well as analytic every where

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: