using limit definition Find the slope of the curve y=2-x^2 at the given point (3,-7) and the equation of the line. include the graph.

Q: Using the limit definition find the derivative of the function f(x)=3x+2.

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Q: two-path test, f has no limit as (x,y) approaches (0,0).

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Q: Computing the Limit of a Difference Quotient In this activity, you will compute the limit of a…

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Q: analyze and sketch a graph of thefunction. Label any intercepts, relative extrema,points of…

A: Given  y=3+2x The intercepts will be 0=3+2x1x=-32x=-23 The x-intercept is -23,0. There is no…

Q: Finding an Equation of a Tangent Line InExercises 37–42, find an equation of the line that istangent…

A: Given: fx=x3+2 The tangent line to graph of fx is parallel to the line 3x-y-4=0. Since the tangent…

Q: (1 point) Let f(x) = 11x² – 3x. (a) Use the limit process to find the slope of the line tangent to…

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Q: Locate any relative extrema and points of inflection. Use a graphing utility to confirm your…

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Q: Finding the derivative by the limit process

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Q: UESTION 4 Write the function in slope-intercept form whose graph satisfies the given conditions.…

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Q: Find a function f that has the derivative f′(x) and whose graph passes through the given point.…

A: Given ,f'x=0and graph of fxpasses through 2,5

Q: Draw a graph to match the description. Answers will vary. f(x) has a negative derivative over (-∞,…

A: we have to write the function that says that  f(x) has a negative derivative over (-∞,-5) and a…

Q: Explain how the real-world meaning of a derivative is related to the independent (input) and…

A: An independent variable a variable that stands alone and it doesn't change by the other variables we…

Q: Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of…

A: Solution:Given             y=x+1x2-4

Q: calculus Find the equation of the tangent line to the graph of f(x) = 4 - x2 at point (1,3).

A: given   f(x) = 4 - x2  point ( 1 , 3 )

Q: Methods used in the Estimation of parameters in a point Estimate

A: Methods used in estimation of parameters in a point estimate

Q: Using the Limit Definition of the Derivative determine the derivative of the function below f(x)…

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Q: ing the limit definition of derivative, find the third derivative of g, given g'(x) = 2-√√x+1

A: Note that, according to Bartleby Guidelines, In the case of multiple questions, we can answer only…

Q: Find the limit, if it exists. If the limit does not exist, explain why. limx→∞ x / √x^2+x+1

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Q: Finding the Derivative by the Limit Process InExercises 1–4, find the derivative of the function by…

A: Given function is: f(x) = 12 We have to find the derivative of f(x) using the limit process.

Q: Find a function f that has the derivative f′(x) and whose graph passes through the given point.…

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Q: Endpoint of (-2 -2) and midpoint (-1½, 1)

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Q: Discuss the relationship between the secant line, slope of the tangent line, derivative of a…

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Q: Comparing Functions and Limits If f(2) = 4, can you conclude anything about the limit of f(x) as x…

A: f(2)=4

Q: Sketch the curve USING CALCULUS. Find all x and y intercepts if they exist, any asymptotes and/or…

A: Here, the given function is: f(x)=x2x2-x Here, the function is not defined at x=1 and x=0. So, the…

Q: Find a function f that has the derivative f′(x) and whose graph passes through the given point.…

A: It is given that the derivative of the function f'x=4.

Q: Finding the Slope of a Tangent Line InExercises 9–14, find the slope of the tangent line tothe graph…

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Q: Puestion 4. Using the definition of the derivative, show that f(x) = ifferentiable at x = -3. |2x+6|…

A: we have to show

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: The chain rule is used to differentiate a function which is the multiplication of two functions. Let…

Q: Finding the Slope of a Tangent Line InExercises 9–14, find the slope of the tangent line tothe graph…

A: Given, The function f(x)=2x2-3  The curve can be differentiated to find the Slope of the tangent.…

Q: (5x²+4)

A: ddx15x2+43

Q: Using the Limit Definition of the Derivative determine the derivative of the function below ?(?) = 5…

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Q: y = 2x – 5 on interval ( - 0, 0)

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Q: 2. Find traits and sketch the graph the equation for a function g (æ) that reflects the function f…

A: Note that, to reflect a function fx over the x axis, find -fx. Here, the given function is…

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

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Q: Limits of Infinity

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Q: (a) Use the limit process to find the slope of the line tangent to the graph of f at x = 2. Slope at…

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Q: Locate the relative extremum and point of inflection. Use a graphing utility to confirm your…

A: Given, function is Now

Q: Find a function f that has the derivative f′(x) and whose graph passes through the given point.…

A: Given: f'(x)=2x  At (1,0)

Q: the slope of the graph of the function at the given point. Use the derivative feature of a graphing…

A: Explanation and solutions is given below.....

Q: linear function that contains the points (3,9) and (12, 12). point-slope form: slope-intercept…

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Q: Find the slope of the curve y=2-x^2 at the given point (3,-7) and the equation of the line.

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Q: Locate absolute extrema Question Given g(x) = = -2x- + x – 1, find the absolute maximum value over…

A: Absolute maximum or minimum of a function in a clsoed interval exist at a point where its first…

Q: Using the limit definition of the derivative of a function at a point, show that the function f(x)=…

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Q: Use an example to show how to use the Second Derivative Test for critical points.

A: Consider a function f(x)=-2x3+36x2-210x+8

Q: reasing or decreasing. Use a graphing utility to verify your results. (Enter your answers using…

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Q: Finding a horizontal tangent line Determine whether the graph ofƒ(x) = xx, for x > 0, has any…

A: Given: y= f(x) = xx , for x>0               Now,                                      lim  x→∞…

Q: When solving a first derivative test, a student calculates the following Help them list all relative…

A: x=-3 and x=8 are critical points means on these points there are local extremas. Given that:…

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

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Q: a) Use the limit definition of the derivative to find the derivative of the function with respect to…

A: Given, To find a) Use the limit definition of the derivative to find the derivative of the function…

Q: Derivative 2. Use the chain rule to find the derivative of f(x) = (3x² – 9)-4

A: Given:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.