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Q: 17. Find all values of the constants m and b for which the function [sin x, mr + b, 12T is a.…

A: Consider the give function y=sinx,          x<πmx+b,      x≥π Since the function fx is continuous…

Q: -. For the function f, f '(x) =x² -1 and f(4) = -1. What is the approximation of f(3.9) found by…

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Q: 10. The slope of the tangent line to the curve y(cos x)+e' =5 at the point where x= is (5+In 5) In5…

A: The slope of a  tangent line of a curve at any point will be equal to the slope of the curve at that…

Q: Suppose L is the tangent line of y 3 tan a 2 csc x at x = Where does L intersect the x-axis? 40 O At…

A: topic - equation of tangent line

Q: 7) Calculate the slopes of the following functions at the given points: Ta) f(x) = ln (x²-x + at IL)…

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Q: Suppose f(x) is the function such that for a > 0 we have f(x) = (e" – 1) In(x) and for x < 0 we have…

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Q: Answer the following questions for the function f(x)=sin^2(x^2) defined on the interval…

A: We are answering only the first three subparts as per our honor code. The function f(x)=sin2x2…

Q: ation: tanh’(x² + 3y 3

A: We have to find dydx of following equation. tanh3(x2+3y3)+ex2y4=3        ........(1)

Q: evaluated at x = 0.001 and y = 0.002 Compute the derivative of the following: 5 g(x) =, 2.1'x f(x) =…

A: topic - derivative of a function

Q: Differentiate the following functions in derivative and differential forms: f,(x) = Ax f,(x) = In x…

A: For f1(x)=Ax ⇒f'1(x)=Adxdx⇒f'1(x)=A Sketch of f1(x)=Ax limx→∞A=A

Q: use the definition to find the derivetive of feconction fcx) = 「X+/ and obtain Hりe equabion of ナんe…

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Q: Answer the following questions about the functions whose derivativesare given:a. What are the…

A: Given: And

Q: Find values at x where the fuction is NOT differentiable(in any) f(x)= lx-2l +3

A: Given function is By definition, we have Therefore,

Q: Note that the solution of the DE: y(x) = e* (S e*~*dx +C) contains an anti derivative which has no…

A: Note: As there is not any point as d. So we cannot solve question h.. Here is the solution of f…

Q: Differentiate the following functions: S(x)= sinh* (v7x +1 tanh " (x* +2) +1) tanh" (x* +2) 3 a) b)…

A: Note    We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 7. For what value of the constants A and B is the function f continuous on (-0o, 0)E AV-x+6-1 for x…

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Q: -1 The tangent line to the graph of y = tanh (4x) is parallel to z + y = 5 at point(s) where

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Q: 1. Find the derivative (dy/dx) of the following functions: In a) y = 3x7- 7x³ +21x2 In b) y = (x2 +…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the…

Q: 11 Find /(x) if ƒ (1) = and the tangent line at (x, f (x)) has the slope 1 1xe*²-1 1 Oa. O b. 1le*-1…

A: Using formula of slope of tangent &amp; integration to find f(x)

Q: Suppose that the first derivative of f(x) = x² In x is approximated by the following formula f'(x) ≈…

A: Note: According to Company Guidelines we are providing the answer of first question. Kindly post…

Q: Suppose that f (x) has a continuous second derivative f"(x), f(2) = 4, f'(2) = –1, and / f(x) dx =…

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Q: I Find the second derivative(y") of the following functions and simplify the final results. 1. y =…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: 2r+19 Find all values of x at which the tangent line to the curve y = x+9 has the y-intercept 2.…

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Q: Q1: From the given graph of f(x) = sin x; [0 ,27] , f ind: (a)The critical points. 211 -2…

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Q: 1. Consider the following function: y = f(x) = ln (2.x² + 6x +5), for r2 %3D (a) Calculate f'(0),…

A: The given function is y=f(x)=ln2x2+6x+5

Q: .4. The approximate value of y=V4+sin.x at x=0.12, obtained from the tangent to the graph at x = 0,…

A: 14)  y=4+sin xy=4+sin x12 Differentiate with respect to 'x' As,  dxndx=n xn-1d sinxdx=cos x…

Q: 6. Find all values of x in the interval [0, 2 n] for which the slope of the tangent to y e* csc(x)…

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Q: 3. Suppose that {f(t)} = F(s) with F a differentiable function and that L{f'(t)} Exists. Then…

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Q: Answer the following questions about the functions whose derivativesare given:a. What are the…

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Q: 25. Use the definition of differentiability to prove that the following function is differentiable…

A: First let us find the partial derivatives of the given function f(x,y)=x+y as shown below:…

Q: Suppose that f is a differentiable function with f(2) = 5 and f'(2) = 7. Let h(x) = f(e*). Find an…

A: Find the derivative for the function h(x). Now, the derivative for the function is the slope for the…

Q: 1. The slope of the tangent line for the function f (x) = In x at x = 1 is: (A) (B) 1 (C) 0 (D) None…

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Q: Find the values of x where the tangent line is horizontal for f(x) = 3x- 2x-9. %3D O A. x-0, x= ОВ.…

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Q: 5. Suppose the function g is defined by g(z) = { kz+1 for 0 < x< 3 for 3 <r < 5, mx + 2 where k and…

A: Given function is g(x)=kx+1  ,0≤x≤3mx+2 , 3&lt;x≤5 limx→3-f(x)=limx→3-kx+1=2k…

Q: If b > 3 and average value of f(x) = 6x – x² on the interval [0,b] is 6, then what is b equal to?

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Q: 1. Consider the following function: y = f(x) = ln (2x² + 6x + 5) , for x > 0 (a) Calculate f'(0),…

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Q: If g(g(x)) is continous at 0, then g(x) is continous at 0.  True or False?

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Q: Let T= f(x,y) be the temperature at the point (x, y) on the circle and suppose that on the circle x…

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Q: 1. Find for differentiate each of the following functions. dy хр a) (In(coshx) sinh x) g) y = - b) y…

A: Given: a)lncoshx3c)y+4coshx2=exsin-1(2x)g)y=sinhxex

Q: The graph of the function f(x) = sin(x+ 8) is shown along with the points (– 8, f( – 8)) and (– 7,…

A: (1) f(x)=sin(x+8)f'(x)=cos(x+8)slope =f'(-8)=cos(0)=1equation of tangent at…

Q: 1. Differentiate each of the following functions: a) f(x) = e³ + (e³)* + sin¬1(x²) b) y = xcos x for…

A: In mathematics, the derivative of a function of a real variable measures the sensitivity to change…

Q: 15. Consider the following common approximation when x is near zero. a. Estimate f(0.2) and give the…

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

Q: (1) Locate the absolute extrema of the function on the closed interval. (a) y=4 sin x, [0,2n] (b)…

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Q: 1. Suppose that g(x) > 0 for all r, g(x) has a continuous derivative, g(-2) = 5 8 g(4) = 3 and |…

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Q: 2. The function (x) = x² is differentiable at x = 1. Find the function & such that o(x) = o(1) +…

A: Introduction: A technique for determining a function's derivative is differentiation. Mathematicians…

Q: 3. Evaluate the following derivatives: a) y = In[sinh(2x)] b) f(t) = tanh-1 VE

A: Derivative of the inverse hyperbolic function formula: -  ddx(sinhx)=coshx ddxtanh1x=12ln1+x1-x…