a) Use the limit definition to find the derivative function, h'(x), of the given function h(x). 2 h(x) 5- x b) Find the equation of the tangent line to the graph h(x) at x = 7. [Hint: Use the derivative in part a) to find the slope of the tangent line].

Q: 1. FIND THE SLOPE OF THE TANGENT LINE TO THE GRAPH OF THE FUNCTION f(x) = 5 – x² AT (3,–4).

A: f(x)=5-x2 To find the slope of tangent, we can use two alternatives (1) Direct derivative (2)…

Q: 1. Find the slope of the tangent line to the graph of f at x = 4, given that f(x) = -x2 + 4Vx.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find an equation of the tangent line to the graph of the function                      y = arctan…

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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) =…

A:

Q: Find the equation of the tangent line to the graph of y at (2, 금). Use the limit process in finding…

A:

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

A: Here the given function  hx=x+2, c=-2 The function can be written as hx=x+2,x≥-2-x-2,x≤-2

Q: 3. Determine the slope of the tangent line to the curve f(x) = at (2x + 1)2 x = 1 by using the…

A:

Q: Prove, using the definition of derivative, that if f(x)  = Cps x,then f'(x) =- Sin x

A: Given fx=cos xBy definition of derivativef'x=limh→0 fx+h-fxhfx=cos xThereforef'x=limh→0 cosx+h-cos…

Q: Find the equation for the tangent to the curve at the given point using the limit definition of…

A: Find the equation for the tangent line to the curve at the given point by using the limit definition…

Q: Use the definition of the derivative to find the value of f'(2) if f(x)=x'-2x. Then use it to write…

A:

Q: 1) Use the limit definition to find the derivative of the function f(x) = 3x – 5x?. Then find all…

A: Derivative of the function in terms of limit is f'(x)=limh→0f(x+h)-f(x)h

Q: Find f(x) if f(2) = 3 and the tangent line at x has slope (x - 1)e** - 2x. f(x) = 1)et?

A: We have to find the function

Q: Discuss the relationship between the derivative dy/dx and (Lim) with drawing if it is required ?

A: See the attachment

Q: Find the slope of the tangent line to the graph of the given function using the limit definition of…

A:

Q: Use the limit definition of the derivative to prove the following special case of the Quotient Rule:

A: We have to prove the following derivative by using limit definition: ddxfxx=x f'x-fxx2 We know for…

Q: Find an equation of the tangent line to f(x) = x² at the point (3,9).

A:

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

A:

Q: 2. Find the points on the graph of f(x) =- where the tangent line is horizontal. x2+2

A: Given f(x)=xx2+2we want to find the point on curve where tangent is horizontal

Q: 3. Use the limit definition of the derivative to find the equation of the tangent line to the curve…

A:

Q: How do you solve question 9?

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Q: Find the equation of the line tangent to y = at the point (-2,1) 2x2 +1 Show all work. (You must use…

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Q: 2) NOT use the short cut method). Use the result to find the slope of the tangent line at the point…

A: Topic:- Derivative

Q: 2. Sketch the graph of a tangent line of the function f(x) = at x = -1. And then find 1- x the…

A:

Q: Find the derivative of the following function using the Limit Definition of the Derivative: f(x) =

A: The given function is:f(x)=3x2To find its derivative using limit

Q: Suppose 8 (x) =sec='(x<). what is the derivative of g with respect to x?

A: We can find the answer as below.

Q: Find the tangent line to the graph of f(x)=(x+1)/(x-1) at the point (2,3)

A: As we know that; The slope of the tangent line to the curve at a given point is equal to the first…

Q: Find the derivative y using limit  definition y=6x^2 +4x

A:

Q: Use the limit DEFINITION OF A DERIVATIVE to find the derivative of the function. 16) f(x) = Vx + 5…

A: The derivative of a function y=f(x) is given by f'x=limh→0fx+h-fxh. The given function is fx=x+5.

Q: 1) Find the slope of the tangent line to the graph of f(x) = x2 - 3 at the point (2, 1). %3D (8…

A:

Q: Prove, using the definition of derivative, that if f(x) = cos x then f ' (x) = - sin x

A: we have to prove by using the definition of derivative that if f(x)=cosx then f'(x)=-sinx   as we…

Q: Find the slope of the tangent line to the graph of f(x) = x2 + x at (2, 6).

A: Given :fx = x2+x

Q: 3) Use the definition of derivative (do NOT use the short cut method) to find_ƒ'(x) given that f(x)…

A: This question is based on finding slope using definition of derivative.

Q: Find f'(x) using the limit definition of derivative.

A: We have given,

Q: 3. Find the equation of tangent line of the function f (x) = e" /x at the point æ 1. Write in the…

A: Given,  The function   fx = exx   We have to find the equation of the tangent line at the point x =…

Q: 4. Find the tangent line to the function f(x) =;xVx² + 5 at the point (2,2).

A: Tangent line of a function:  Differentiate the equation of the curve Substitute the value into the…

Q: :) Given f(x) = |x|+x, at which point does the derivative not exist? Mathematically Question 4 (-…

A: We are given a function fx=x+x and we have to find the point at which fx is not derivable. We know…

Q: .. Consider the quadratic function y = 4-x². Using the limit definition, ind the derivative of the…

A:

Q: Find the equation of the tangent line to the graph of f(x)= x ln(2x+3) at the point (-1,0).

A:

Q: 2. Use the definition = f'(x) = limw-x- S(w)-r(x). to find the derivative of w-x y = tan x.

A:

Q: 12. (a) Use the definition of derivative to find the slope of the tangent line to the curve f(x) =…

A:

Q: Find the derivative of the following functions using the limit definition. 1. y = x² – 4x – 5 -

A:

Q: 1) Use the limit definition to find the derivative of the function f(x) = 6x – x². Then find all…

A: Using limits definition:f'(x) = limh→0 f(x+h) - f(x)hf(x) = 6x - x2f(x+h) = 6(x+h)- (x+h)2   = 6x +…

Q: Find the derivative of the following functions using the long method (limits)

A: Given: x= 12 t4-5t-3 To Find: limh→0xt+h-xth

Q: 1 Use the limit definition of the derivative to find f'(x) if f (x)= 10x

A:

Q: 1. Use implicit differentiation to find the slope and equation of the tangent line given f(x) = x³…

A: Given function is  f(x) = x^3+y^3-9  According to Bartley guidelines we can attempt only one…

Q: B) Use the definition of differentiation to find the derivative of the function f(x) = 4- Vx + 3. Is…

A: Consider the function: fx=4-x+3 The definition of derivatives is given by the formulas,

Q: 3. Find the siope of the tangent line that crosses through the point (3, 7) along the 2 curve f(x)=x…

A: Given :f(x)=x2-x+1

Q: suppose the derivative of f exists, and assume that f(2)=3, f'(2)=4. Let g(x)=x^2f(x) and h(x)=…

A: The objective is to find the equation of tangent lines of g(x) and h(x) at x=2

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: