Estimate f(5.09) for f as in the figure. y y=f(x) (10, 4) Tangent line (4, 2) (Give your answer to three decimal places.)

Q: Estimate the slope of the tangent line of the function f(x) = 2e* at the point x = e. %3=

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Q: Find the equation of the tangent line to the curve f(x) = a² + 2x at x = 1. Enter the answer in the…

A: f(x) = x2 + 2x      at x=1  y = x2 + 2x   At x=1  =>  y = 12 + 2(1) = 1 + 2 = 3 point on the…

Q: Find the gradient of the tangent line to y when x = 2.

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Q: Which of the following is the derivative of * f(x) = In(tanhz)? %3D

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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: y = x*lnx %3D %3D

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Q: Use differential to approximate the change in y=x3+x2 as x changes from 1 to 0,95.

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Q: What is the equation of the tangent line to the function y = e-* – arcsin( 2 at x= 0 ? A) y - (1+) =…

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Q: df Use derivative rules to compute where f(x) = -2xe". dx x%3DIn 7

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Q: Estimate the slope of the tangent line at the point t= -2 for f(t) = 6t-3 (Give answer as a…

A: The given function is f(t)=6t-3 at t=-2

Q: Find the equation of the tangent line to the graph of y = f(x) at r = 3. %3D f(x) = In(x – 6|) y =

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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: What is the derivative of f(x) = - 3 with respect to r? %3D

A: Given: The function f(x)=-3x3

Q: What is the derivative of f(z) = cosh(r) + sinh(r)?

A: To find the derivative of  f(x)=coshx+sinhx

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: Hiwofind the derivative of the function fwith respect to Vaniable t,, tz when ti-l, tz=3 2. X=Lncti)

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Q: Determine the value(s) of x such that f(x)=e*-6x have a horizontal tangent line. Answer in exact…

A: Given that  function f(x) = e3x - 6x and we determine the value of x the function have horizontal…

Q: Find the equation of tangent line to the curve f(x) = 2 – dt 1+t at the point x = 1.

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Q: Find all values of x, xe[0,2n] where f(x) = secx has a horizontal tangent line

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Q: Find the equation of the tangent line to the graph of f(x) = Vr+ 81 at the point (0, 9). Answer y =

A: Solution:step 1: given f(x) =x+81at point (0,9)now, point 0,9 ⇒ x1=0…

Q: Find the derivative. F(t) = In(sinh(2t)) %3D F'(t) %3D

A: Find the derivative of the function

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: The slope of the tangent line to the graph of the function y= Ttx- cotx at x=0 is O T+1 O T-1

A: Solution is given below:

Q: CTION is Consider the function y = r(ln z). At which point the tangent line to the graph of this

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Q: Find the (a) approximate error and (b) relative approximate error of the following: The derivative…

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Q: Find the tangent line to the function y = x2 at (1,1)

A: y=x2 Differentiating with respect to x, we get dydx=2x   ∵dxndx=nxn-1 Now slope of the tangent line…

Q: Estimate the slope of the tangent line of the function y(t) = V41 + I at the point t = 1. (Use…

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Q: findsecond derivative d'F/dt 3t°-zf3nd find it ot ct f}=(-!>)

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Q: Use the graph to estimate the slope of the tangent line to y = xn at the point (1, 1). Verify your…

A: Given curve is y=x-1. Power rule of differentiation states that, ddxxn=nxn-1 Differentiating the…

Q: Find the eguation for the tangent line to y = fcx) at the specified point. fcx)= xe-X ; where X=O ノ

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Q: se the quotient rule to find the derivative Vt p(t) = %3D 4t-3 (t) =D %3D

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Q: Use the graph to estimate the slope of the tangent line to y = xn at the point (1, 1). Verify your…

A: Estimate the slope of the tangent line to y=x12 at the point (1, 1) and then verify the answer…

Q: Find the equation of the tangent line to the function f(x)=2x2-x  at the point where x=−1. Give your…

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Q: Determine the equation of the tangent line to the function g(x) = (2ex)/x at the point, (2, e2).

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Q: Find the slope of the tangent line to the function f(x) = tan(cos(ax)) at x =π/2a. Leave your answer…

A: According to chain rule of differentiation ddxfgx=f'gx·g'(x) . Now using this rule differentiate the…

Q: Find the derivative of the function f(x,y) = tan at the point (3, - 3) in the direction in which the…

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Q: Find the derivative of y(x): :/ sec(re')dt . Evaluate both y and at x = 0. dr

A: Explanation of the solution is given below...

Q: Find the derivative of the function. F(x) = et dt F'(x) = %3D

A: We know that by Leibniz rule of differentiation under integral sign, we have

Q: Estimate f(5.06) for ƒ as in the figure. y y = f(x) (10, 4) Tangent line (4, 2) (Give your answer to…

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Q: Use a tangent plane to approximate the value of the following function at the point (- 2.9, 3.9).…

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Q: Estimate the slope of the tangent line at the point t = -6, for f(t) = 4t – 2. (Give your answer as…

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Q: Find the point(s) on the graph of f where the tangent line is horizontal. F(x)=x/ (x^2+25) smaller…

A: When a tangent line is horizontal there F'(x)=0  We find F'(x) using the quotient rule

Q: Does the graph of the function y = tan x - x have any horizontal tangents in the interval 0 sx <2n?…

A: We get the slope y' of the tangent to the function y=tan x-x by differentiating it with respect to…

Q: at dz = (4자) 424-4%.

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Q: Find the equation of the tangent line to the function f(x) = r + 3z++4 at the point where x =-2.…

A: Given : fx = x3+3x2+x+4

Q: Estimate the slope of the tangent line at the point t = -5, for f(t) = 10t – 1. Give your answer as…

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Q: What is the derivative of f(z) = (z³ –- (z – 1)º)*? %3D

A: Given function is f(x) = (x3 - (x-1)3)3

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: