1. Let f(r) 5r?. %3D (a) Using the limit definition, find f'(3). (b) Find the equation of the line that is tangent to 5a at r = 3.

Q: If the derivative of y = f(x) at x = 2 is equal to " (0 " then y = f(x) is not continuous at r = 2.…

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Q: For f(x) = x3, show that the slope of the secant line over [l,x] is x 2 + x + 1, and use this to…

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Q: Find the slope of the tangent line at a for the graph of the f(x) = xtan z y(x) be given implicitly…

A: a) Here we have to find the slope of the function f(x)=xtanx .......................... (1)  Let…

Q: Suppose that f(x) is differentiable for x > 0, y = 2x + 1 is the tangent line to the graph of f at x…

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Q: Estimate the slope of the tangent line to f(x) = x³ at x=2 by finding the slope of the secant line…

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Q: Let f(x) = 6x + 2 tangent line to the graph of f(x) at the point (0, – 3) is given by y = mx + b for…

A: The objective is to find the equation of the tangent line.

Q: What is the slope of the tangent line that touches the graph of In y + e2=-1 = 3y – 4x at the point…

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Q: he tangent line to y = f(1) at (-3,9) passes through the point (9,-3). Compute the following.

A: The slope of the line passing through the points, (x1,y1) and (x2,y2) is given by .

Q: What is the %ER of the approximate derivative of f(x) = x2ex , using forward-difference %3D approach…

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Q: d. Find the slope of the tangent line to the graph of x +y + xy 3 at (1, 1).

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Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(r) = V9r +…

A: Given:       fx=9x+5 at x=1  Instantaneous rate of change :    If y=fx, the instantaneous rate of…

Q: Defermine the derivative of the following functions using the long method (using limits). 1. y =t –…

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Q: Find the line tangent to the graph of f(x) = cos(x) at xo = T.

A: f(x)= cos(x)  Then, f(π) = cosπ⇒f(π) =-1

Q: use the defin ition of derivative at t he slope of tangent llne of the cuwe f(x)=t at x= | Poiat to…

A: According to the questionF(x)=1x2+5,     x=1

Q: Is there a smooth (continuously differentiable) curve y f(x) whose length over the interval 0sxsa is…

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Q: The tangent line to the curve il me f(a) at 2 m 1 goes through the points y=f(x) x == and Find the…

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Q: If f(x)=sqrt x, find the linearization L(x) at a=4. Thus the graph of L(x) would be tangent to f(x)…

A: Given information: fx=x ,  at a=4 Formula of Linearization  Lx=fa+f'ax-a

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

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Q: Find the equation of the tangent line of f(x) = x⁴ + 2x at x = 1 using the limits definition.

A: The function is fx=x4+2x and x=1.  Find the derivative of the function fx=x4+2x using the limit…

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: is the equation af tangent line at X=/ y = mx+b. to the giaph of f c) =x² -x at x=/ m%= b.

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Q: Let f(z) = VII - z The slope of the tangent line to the graph of f(=) at the point (7, 2) is The…

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Q: Let y = -. Find the values for A and B so that %3D A dy dx %3D xB where A = -1 %3D B = 2 The limit…

A: The equation is y=1x.

Q: Given: f(x)=x2+2 find the equation of a line tangent at point P(1,3) using limits

A: To find the equation of a line tangent at point P(1,3) on below curve using limits.

Q: Why is the limit of the secant line PQ to a curve as it approaches zero is the same as the slope of…

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Q: Find the equation of the tangent line for f(x) = 6 tan(x) at a = %3D a) Oy = 6/3 (z -) + + 12 b) Oy…

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Q: Let L be any tangent line to the curve √x + √y = √c. Show that the sum of the x- and y-intercepts of…

A: The given curve is x+y=c. Differentiate the above equation with respect to x as follows.…

Q: For what vaules of x in the interval [0,2π) does the fraph of g(x)= (√3)x+2sinx+7 have a horizontal…

A: For horizontal tangent,first derivative must be zero

Q: Find the equation of the tangent line (assuming it exists) to f(x) = x² + x at x = -2. Give your…

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Q: 46. Show that the sum of the x- and y-intercepts of any tangent line to the curve Vx + Jy = \c is…

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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 to the curve r+ 2xy + y = 16 at (1, 3). The slope is VEnter undof if…

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Q: y = 3x?+1 ; (0,1)

A: Solution ) slope of the tangent line by the limit definition = m = (dy/dx) [ x = 0 becuase we have (…

Q: 2. Given that y= -- Use a limit to find the instantaneous rate of change of y with respect to x at…

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Q: Let f(x) 2, -) | (- The slope of the tangent line to the graph of f(x) at the point( is The equation…

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Q: 6. Using the limit definition find the derivative of y t2 o IN.

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Q: Find f(4) and f' (4), assuming that the tangent line to y = f(x) at a = 4 is y = -6x + 2. %3D

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Q: The slope of the tangent line to the graoh of y = In x at x = a approaches infinity as a 0t. Select…

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Q: Let y(x) = 2. x+2 Estimate the slope of the tangent line of y(x) at the point a = 0:

A: The given function is: y(x)=1x+2

Q: Show that the sum of the x-intercept and y-intercept of any tangent line to the curve Va+ Vg = Vc is…

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Q: dy at x = 2. dx 2 10. Given the curve y= 5 - (x-2)³, find (A) 3 -- (B) 3/2 (C) 5 (D) The limit does…

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Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

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Q: 7) Use a tangent line approximation with the function g(x)= Jx to estimate V9.2

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Q: Find the slope of the tangent to the curve y-x cos 3x at *- O al o Ob) 1 Od) 3

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Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve…

A: Question is solved.

Q: Suppose that the tangent line to the graph of y = f(x) at x = 2 is y = 4x – 3 and that the tangent…

A: The given tangent line to the graph of y=fx at x=2 is y=4x-3 and the another given tangent line to…

Q: Find t6e eavation of tangent ine of fcx) = X+) at X=2 X-3

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Q: The slope of the tangent line to the graph of x + y + xy = 3 at (1, 1) is Blank 1.

A: Let's find.