Estimate the instantaneous rate of change of P(t) = 2t2 - 2 at the point: t = 3 In other words, choose x-values that are getting closer and closer to 3 and compute the slope of the secant lines at each value. Then, use the trend/pattern you see to estimate the slope of the tangent line.

Q: The derivative of position with respect to time is ... O velocity

A: Velocity is the derivative of position with respect to time.

Q: Estimate the slope of the tangent line of the function y(t) = sqrt(2t+1) at the point t=5.

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Q: Find the equation of the tangent and normal line to the curve y=x2 at x=1

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Q: Find slope of the tangent line to the elipse x^2/36 + y^2/16=1 at the point (x,y) slope=

A: Given ellipse equation is x236+y216=1 find the slope of the tangent line at the point (x,y)

Q: Estimate the slope of the tangent line at the point indicated. P(x) = ex ; x=0

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Q: Estimate the instantaneous rate of change of y(t)=4t^2+5 at the point: t=−1 In other words, choose…

A: Given: y(t)=4t2+5. Now,          y'(t)=8t. At t = -1,           y'(-1)=8(-1)=-8.

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Q: find the equation of the tangent line and normal line to the ff. curves at the indicated point.

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Q: Find the slope of the tangent line to the curve - 32 + 2ry-y = 0 at the point ( 1, – 1).

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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…

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Q: Estimate the instantaneous rate of change of y(x) = 2x² + 2 at the point: In other words, choose…

A: To estimate the instantaneous rate of change of yx=2x2+2 at the point: x=-2.

Q: find the equation of tangent and normal to the curve √ x-√ y=1 at (9,4)

A: find the equation of tangent and normal to the curve √ x-√ y=1 at (9,4)

Q: What is the slope of the tangent line to y = 4x at x = 0?

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Q: Estimate the slope of the tangent line at the point t = -7, for f(t) 6t - 2. (Give your answer as a…

A: Given,

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: If the instantaneous rate of change of fx) at (9, -6) is 2, write the equation of the line tangent…

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Q: Estimate the slope of the tangent line at the point indicated. f ( x) = ex; x=e

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Q: What is the x-intercept of the tangent line to y=ln(x) with a slope of 8?

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Q: Approximate the derivative of y=x at x=1 by forming small changes.

A: SOLUTION:-

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

A: Use the graph to estimate the slope of the tangent line to y = xn at the point (1, 1). and to verify…

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A: The given equation is,

Q: Let f(x) = 6 - 3x + 5x2. (a) Find f'(a) (b) What is the instantaneous rate of change of f when x =…

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Q: 4) Estimate the instantaneous rate of change of function f(x) = x + 5x' +2 at x = -3 b) Determine…

A: Given that fx=x4+5x3+2First, we will find the instantaneous rate of change of the functionat x=-3.

Q: (a) Determine the slope of curve y = x · Ln(x) at x = 3.

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

Q: If the instantaneous rate of change of g(x) at (-1, -2) is 1/2, write the equation of the line…

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Q: At which points on the curve y = 1 + 60x3 - 2x5 does the tangent line have the largest slope? 1 5…

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Q: Determine the equation of the slope of the line tangent to y = tan(x) using the 4-step rule.

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Q: Find the average rate of heating over the first 6 minutes. þÞ By drawing a tangent to the curve,…

A: Given graph represents the temperature (T° Celsius) of a metal ingot as it is heated over a period…

Q: Determine the slope of the tangent line at t = 2

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Q: Find the slope of the tangent and normal to the curve  y=2x2+3sinx at x=0

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Q: For the function y = (x - 5)(x2 - 3x + 1) at (2, -3) find the following. %3D (a) the slope of the…

A: We have to find slope of tangent line and instantaneous rate for change..

Q: If the instantaneous rate of change of f(x) at (4, −3) is 7, write the equation of the line tangent…

A: The objective is to find the equation of the tangent line to the graph of f(x) at x=4.

Q: Find the rate of change of the distance D between the origin and a moving point on the graph ofy…

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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: IL FIND THE EQUATION OF THE TANGENT LINE AND NORMAL LINE TO THE FF. CURVES AT THE INDICATED POINT.…

A: Since you have asked multiple questions and with each question having multiple part i will solve the…

Q: For the function y= x^2+5/x+5 at (1,1), find the following. ( give exact answer. Do not round ) (A)…

A: Given: y=x2+5x+5 ; Px,y=1,1 (A). As we know that, the slope of the tangent line to the curve at a…

Q: Find the slope of the curve y^3+3x^2y-9y=-5 at the point (1,-1) and also find the rate of change…

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Q: Find the slope of the tangent line to the curve `-3 x^2 + 3 xy + 4 y^3 = 8` at the point (4,2)`.…

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Q: For the function  Y=(x^2-8x)/(x^2+7x) at (5, -1/4) find the following. (Give exact numbers. Do not…

A: Given data:   The given equation for the curve is y=(x2-8x)/(x2+7x). The given point is (x1,…

Q: Estimate the slope of the tangent line at the point indicated.

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Q: Find the average rate of change and the equation of the secant line for 2x f (x) = from -1 to 3. x²…

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Q: Q-2- Find the eAuation of the tangent line.and the normal line for the fallowing function X = 0-…

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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: IL FIND THE EQUATION OF THE TANGENT LINE AND NORMAL LINE TO THE FF. CURVES AT TH INDICATED POINT.

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Q: Find the slope of the tangent line to x+y=10 at (1,8).

A: According to our guidelines , we can answer only first question. Kindly re-post other remaining…

Q: Estimate the instantaneous rate of change of P(t) = 5t + 6 at the point: t = 3 In other words,…

A: Given that Pt=5t2+6 To find the instantaneous rate of change of P(t) at point t=3.

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: For the function  y =  x2 + 3 / x+5    at  (2, 1),  find the following. (Give exact answers. Do not…

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Q: Find the instantaneous rate of change cope of the tangent line to 2 (3,-2) 1

A: Since you have asked multiple question, we will solve the first question for you as per our guide…