Use linear approximation, i.e. the tangent line, to approximate 1/0.204 as follows: Let f(x)=1/x and find the equation of the tangent line to f(x) at a "nice" point near 0.204. Then use this to approximate 1/204.

Q: Find an equation of the tangent line to the given curve at the specified point. = (1, e) X y =

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Q: Find a formula for the error E(x) in the tangent line approximation for f(x)=√(1+x) near x=a=0 ?

A: Differentiate the function f with respect to x, to find f'(x). Substitute 0 for x in fx=1+x and…

Q: Find the equation for the tangent line to the curve y = f(x) at the given x-value. f(x) = (2x + 3)“…

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Q: Find the equation of tangent line of the function f(r) = e"/x at the point a = 1. Write in the form…

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Q: Find the equation for the tangent line to the curve  y = f(x)  at the given x-value. f(x) = x ln(x…

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Q: Find the equation of the tangent line to the function f(x) = e*-1 In(x + 1) when x = 0.

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Q: Find the slope of the tangent line to the curve y =1+x+x´at the point x = a.

A: The curve is y=1+x+x2. Differentiate the function: dydx=1+2x

Q: Find the tangent line to g (x)

A: Given, g(x)=16x-4x

Q: Find the equation of the tangent line to the graph of f(x) = In x at xo = e 8.

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Q: Find the equation of the tangent line to the graph of f(x) = x'e- at x = 0.

A: The given function is f(x)=x9e-x at x=0.

Q: Find the equation of the tangent line to f at x = a. f (x) = x2 + x, a = 1

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Q: Use linear approximation, i.e. the tangent line, to approximate 0.252 as follows:

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Q: Find the equation of the tangent line. to y=f(x) at point P. %3D

A: We have to find the equation of tangent to y=f(x) at P.

Q: Find an equation of the tangent line to the graph of f(x) = xe¯X at its inflection point. y =

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Q: Find the exact equation (without decimal approximations) of the tangent line in the form y = mx + b…

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Q: Find the tangent line to the function y = x^2 at (1,1).

A: The given function is: y=x2 Now differentiate it with respect to x: y'=ddxx2y'=2x Put x=1 in y' to…

Q: Find an equation of the tangent line and normal line to the curve given by f(x) = x? – 6x + 5 at the…

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Q: Find an equation of the tangent line to the curve at thegiven point  y =  e x  / x…

A: Given curve is y=exx To find: Equation of the tangent line to the curve at point (1,e). Solution:…

Q: Consider the function f(x) = 1/x and show it on grap. Find the equation of the tangent line at x =3.

A: Given function is fx=1x. To graph the function and the find the equation of the tangent line at x=3.…

Q: If the tangent line to the graph of y = f(x) at x = 3 is horizontal, what is the derivative of f at…

A: Slope of the tangent line of the graph y=f(x) is dy/dx=f'(x) Slope of the tangent line at x=3 is…

Q: Find the equation for the tangent line to the curve y = f(x) at the given x-value. f(x) = (4x + 5)5…

A: Given equation of curve is as below. To find the equation of tangent line to the curve f(x) at x =…

Q: Find the tangent line to f(x) = ax³ at x = -1. Assume that a is a positive constant. ***

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Q: Find the equation of the tangent line to the following curve at the given point y = cosh(x) + e3when…

A: we have to find equation of the tangent

Q: Find a > 0 such that the tangent line to the graph of f(x) = x 2e-x at x = a passes through the…

A: fx=x2e-x Differentiating with respect to x, we get f'x=dx2dx·e-x+de-xdx·x2=2x·e-x-e-x·x2=x e-x2-x…

Q: Find the equation for the tangent line to the curve  y = f(x) at the given x-value. f(x) = ex3 − 1…

A: To find the slope of the tangent at x=1 we have to find f'(1) So, slope = 3

Q: Find the equation for the tangent line to the curve  y = f(x)  at the given x-value. f(x) = ex5 −…

A: The equation for the tangent line to the curve: (y - y1) = m(x - x1) m = f'(x)

Q: Find the point on the graph of f(x)=ex for which the tangent line to the graph there passes through…

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Q: Find the equation for the tangent line to the curve y=f(x) at the give x-value. f(x)=ex^2-1 at x=1

A: equation of the tangent at the point ( x1,y1) with slope  y - y1 = slope ( x - x1)

Q: Find the slope of the tangent line to the graph of yx? + xy = 2 at (1, 1)

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Q: Find the slope of the tangent line to f(x)=ex at the point (1, e).

A: Given,         The slope of the tangent line to fx=ex at the point 1,e.

Q: Use the fact that derivative of a function at a point is the slope of the tangent line to the graph…

A: We know that the derivative is 0  at the maximum and minimum point on the graph  From the graph we…

Q: f(x) = ln(x − 1) at x = 2

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Q: Use linear approximation, i.e. the tangent line, to approximate 0.252 as follows:

A: Linear approximation for a function at x=a is

Q: Find the equation of the tangent line to the curve f(x)= Va. Assume f'( x) 1 at x = 4.

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Q: Find the x-coordinate(s) of the point(s) on the graph of y = x + sinx at which the tangent line has…

A: Graph of y=x+sinx

Q: Find the tangent line to y = f(x) at the point (0,–5).

A: We have to find the equation of tangent from the curve f(x) and point

Q: Use linear approximation, i.e. the tangent line, to approximate v81.1 as follows: Let f(x) = Vx.…

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Q: Find the equation for the tangent line to the curve  y = f(x)  at the given x-value. f(x) = [(x −…

A: Consider the given function.

Q: Find the slope of the tangent line to the graph of the function at the given point.    f(t) = 3t −t2…

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Q: Find an equation of the tangent line to the curve x e y + y e x   = 1 at the point ( 0, 1)

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Q: Find the equation of the tangent line to the following curve at the given point. y = cosh(x) +…

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Q: Find the point on the graph of f(x)=ex for which tangent line to the graph there passes through the…

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Q: Find an equation of the tangent line to y = f (x) at x = a.

A: The derivative of a function at a point gives the slope of the tangent to the curve at that point.…

Q: Find the equation for the tangent line to the curve y = f(x) at the given x-value.   f(x) = x ln(x…

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Q: Find an equation for the tangent line to the following curve, h(x) = 16x – 2 In x at the point where…

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Q: Find the equation for the tangent line to the curve  y = f(x)  at the given x-value. f(x) = (2x +…

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Q: The slope of the tangent line to the graph of y = e3 at x = In 2 is

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Q: Let F(x) = et? e dt. Find an equation of the tangent line to the curve y = F(x) at the point with…

A: Equation of tangent line is y=mx+b where m is the slope  To find slope we take derivative of F(x)…

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: