113120 Example 1: Tangent line approximation Find the tangent line approximation of: SUpe f(x) = x-2x +3 @x=2 3nopnst on belliso at bae 2.2 2.1 1.99 2 2.01 1.9 1.8 Inslendu a elo eauctse f(x) = Y

Q: 7² – 1 esec z Find the slope of the tangent lint to the curve y = /2 dt at r = 2

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Q: 1. Find an equation of the tangent line to the curve at the given point. (a) y = In(x? – 3x + 1) at…

A: Since you have posted multiple questions i can do first question (both subparts) as per our company…

Q: Consider the curve described by the relation y + eV= x* - x² + 1. Find an equation of the tangent…

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Q: 1 0.204 as follows: Let f(x) 1 x Use linear approximation, i.e. the tangent line, to approximate the…

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Q: An equation of the tangent line to the graph of f(æ) = (e¯")² at a = - In 2 is Select one: O a. y +…

A: As per company's norm we are allowed to solve only one question at a time. Repost the rest question…

Q: 1 as follows: Let f(x) 1 and find Use linear approximation, i.e. the tangent line, to approximate…

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Q: Let f'(x) = e and g(x) = f(Vx). Let L denote the slope of the tangent line to the graph of the…

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Q: Find the equation of the tangent line to the graph of the function f(x) = 30 - 4In(2) at I = 1.…

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Q: An equation for the tangent line to the curve In(sec x + y?) = tan(x)+e2" – 1 at the point (x, y) =…

A: Given curveIn (sec x +y2) = tan x +e2x-1We have to find the equation of tangent line at the point…

Q: x Suppose the slope of the tangent line at any point on a curve is x²+4y² If the curve passes thru…

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Q: 11.Determine the equation of the curve whose tangent line at any point (xy) is e* – sin x and passes…

A: Given problem:- Determine the equation of the curve whose tangent line at any point (x,y) is ex -sin…

Q: 4 sin x Let f(x) = 2 sin.x + 6 cos x Then f'(x) = The equation of the tangent line to y = f(x) at x…

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Q: Use linear approximation, i.e. the tangent line, to approximate 3.6^7 as follows: Let f(x)=x^7. The…

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Q: 3. Let f(2) = 1+ 2e" – 3x. At what value(s) of a does f(x) have a horizontal tangent line? Give…

A: Differentiating given function with respect to x, we get

Q: 3. Let g(r) - r'e". Find all values of a where the tangent line of g(z) is horizontal.

A: To solve the following where tangent line is horizontal

Q: Find the derivative of TC y = In sin-1 e Gr sin- G) + eln sin- () [T x sin¯ In sin-1 1 · (In 4 – In…

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Q: Use linear approximation, i.e. the tangent line, to approximate 998 as follows: Let f(1) = 1 The…

A: We have to solve

Q: written

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Q: Using the Newton Raphson method, if the curve f(x) is constant then the slope of the tangent drawn…

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Q: Find a > 0 such that the tangent line to the graph of f(x) = x?e=* at x = a passes through the…

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Q: Verify the given linear approximation at a = 0. Then use a graphing calculator or computer to…

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Q: Use linear approximation, i.e. the tangent line, to approximate 1/1.001as follows: Let f(x)=1/x and…

A: Given problem:- Use linear approximation, i.e. the tangent line, to approximate 1/1.001as follows:…

Q: (a) What is the derivative of sin t? d sin t dt (b) The velocity of a particle at time t is v(t) =…

A: (a) From the given problem:   ft=sint   So,   dftdt=ddtsint=cost...we know that:dsinxdx=cosx   Hence…

Q: cal linear approximation of f(x) = √ (1+x) at x0 = 0. Use your approximation formula to approximate…

A: The given function is f(x)=1+x at x0=0 we have to Find the local linear approximation.

Q: 11. Find the rate.cf.changf.f.at.P.in.the directod then.vectoe ūf a. f.=ylnx. P(1,-3. --3 P.(I,-3..…

A: Directional derivative

Q: The slope of the tangent line x= e, y= In e3x %3D 3er 3e-3r K OR 3e none of the above

A: Given:    x = ex , y = ln e3x

Q: a) The tangent line for y = f(z) at the point (c, f(e)) has as its equation y = f(c) + f'(e)(r – e).…

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Q: 4 sin x Let f(x) = 2 sin x + 4 cos e 4 Then f'(x) = (sin (z) + 2 cos (2)) The equation of the…

A: We are given,                 And we have found               . So, the slope of the tangent line…

Q: x² + 1 Find the tangent line of y = at r = 1

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Q: A bar is insulated at end x =0, and open to the ambient temperature at end x =2L. There is a heat…

A: The solution to the above question is in the images below.

Q: Use linear approximation, i.e. the tangent line, to approximate ^3√64.2 as follows: Let f(x) = ^3√x.…

A: where, m is the slope of the line and where b is the y-intercept.

Q: The positive value of x at which the graph of y=1/x has a tangent line parallel to 4y= -x+3 O 1 O 2…

A: To find the slope of the tangent line to the graph of y=1x, differentiate the function, with respect…

Q: let a>o be a fixed real number. Let acoscx?3+ X ln cy) = y2+2xy+ & -1 find the equation of the…

A: the given equation of the curve is: a2cosx2+xlny=y2+2xy+a2-1 we have to find the equation of the…

Q: Find the tangent line approximation for f(x) = V2 – x at x = -2. Use it to estimate the value at x =…

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Q: Use linear approximation, i.e. the tangent line, to approximate /25.2 as follows: Let f(x) = VE.…

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Q: 2 sin x Let f(x) 4 sin x + 6 cos x Then f' (x) = The equation of the tangent line to y = f(x) at a =…

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Q: 1. Find the equation for the normal and tangent lines for f(x) at the specified points. a) f(x) = e…

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Q: The graph of y = f(x) is shown below as the solid curve. The tangent line to y = f(x) at the point…

A: Question is solved.

Q: Use linear approximation, i.e. the tangent line, to approximate 1.3 as follows: Let f(x)=√x. The…

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Q: Consider the function  f(x) such that (a)  f(1)=1/ln^2 and (b) the tangent line at  (x,f(x))  has…

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Q: Use linear approximation to approximate√25.4 as follows. Let √f(x)=x. The equation of the tangent…

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Q: An equation of the tangent line to the curve y = sin(z) at x = 1/6 is y = -(z – 7/6) . An equation…

A: a.

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

A: Given that

Q: Let g(x)= arctan(x^3 + 3x^2 - 9x). Find all values at which g(x) has a horizontal tangent l

A: Given the function g(x)=tan-1(x3+3x2-9x). We need to find the values at which g(x) has a horizontal…

Q: Define g(z) = ze". Find the tangent line for g at x=1. If it is in the form y3mx+b, what is the…

A: 1) Consider the given function, gx=xexg'x=ddxxex=xddxex+exddxx=xex+ex1=exx+1   The slope of the…

Q: 1 approximate Use linear approximation, i.e. the tangent line, to 1 and as follows: Let f(x) - 0.504…

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Q: JA string of length l has a zero initial velocity and a displacement yo(x) as shown. (This ini- tial…

A: Given: A string having the length l having a zero initial velocity and displacement as shown in the…

Q: 1 as follows: Let f(x): 1 and find Use linear approximation, i.e. the tangent line, to approximate…

A: A nice point near 0.203 is 0.2  f(x)=1xf'(x)=-1x2At x=0.2f(0.2)=10.2=5f'(0.2)=-10.22=-25 This means…

Q: A particle moves along the x-axis so that its velocity at time 0 <t<18 is given by v(t), whose graph…

A: We are given the graph of the velocity function v(t) We know that when the slope (derivative) of…