Determine the continuity and, if discontinous, the type of discontinuity for the function h(x)=(x^2-1)/(x+1) at x=-1.

Q: Suppose that lim (x,y)→(3,1) f(x,y) = 6. What can you say about the value of f (3,1)? What if f is…

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Q: use the limit definition of a derivative to find f'(x) f(x)= sqrtx+5

A: See the details solution in below

Q: Find the derivative of the function by the limit process. f(x) = x2 - 2 %3D f'(x) = 2x %3D Need…

A: Apply Limit rule

Q: Determine the derivative of the cube root function f(x)=3√x using the limit definition.

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Q: 5. Use the limit definition of derivative to find f'(x) if f(x) = VT.

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Q: Find the equation of the tangent line to the function f(x)= x^3-4x at the point where x=0. Do not…

A: Here first we find the slope using the formula m=f'0 Then equation of the tangent at point x = 0,…

Q: Calculate limh→0 f(x+h)-f(x) for f (x) = /2x+3. %3D h f(x+h)- f(x) /2x+3 limh0 h -2(2x+3)…

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Q: f(x) = /x +5

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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: If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

A: The detailed solution is as follows below:

Q: Give an example of a function that is continuous but differentiable at x=2

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Q: Use the limit definihon of the that gex)= derivative to show 9(x)= 3 3 has denvahre X+5

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Q: Use the alternate definition, lim Ax)-Aa) to determine the instantaneous rate of X- a change of Ax)…

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Q: Give an example of a function that is continuous on -∞ < x < o but is not differentiable at x = 3.

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Q: Use the definition of the derviative to compute the derivative of f(x)=1−3x2f(x)=1−3x2 at the…

A: Use the definition of the derivative to compute the derivative of f(x)=1−3x2 at the specific point…

Q: how would you, using a limit def. of a derivative at a point find f'(-1) for the function f(x). =…

A: Hint:

Q: If the function is defined y=2x when x=3, is this function differentiable at x=3? Also, is this…

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Q: Evaluate limit as x approaches 0 from the right of (1+x)cotx

A: Given, limit expression

Q: Compute for f '(3) using the limit definition of derivative if f(x) - 6x²

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Q: Find the derivative of the function f(x)=2x2 using the limit definition.

A: Limit definition of derivative of f(x) is  f'(x)=limh-&gt;0f(x+h)-f(x)h

Q: x² – 16 f (x) = x( x 2(х — 1)°(х — 2) : о 1)8 (x – 2) : 0 - -

A: If the given function is equal at LHL and RHL at x=3 then the given function is continuous at x

Q: Let f(x) = Cx + 7x if x< 4 x³ - cx if x2 4. For what value of the constant c is the function f…

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Q: Use derivative to identify open intervals on which the function is increasing or decreasing.…

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Q: 2 Find the derivative of f(x) =x² – 6 from limit definition. - Show all steps of working. f(x) :…

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Q: Use the limit definition of the derivative of a function to find the derivative of f(x) = 4x at x-5

A: From the given problem:   fx=4x2   From the limit definition of the derivatives:…

Q: Use the limit definition to find the slope of the tangent line to the graph of f at the given point.…

A: Find the slope.

Q: Show with the middle value theorem that the second derivative f'′ has at least one zero (for this…

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Q: 2) Use the definition of the derivative, f'(x) = lim Ax-0 derivative of f(x) = 5x² + 3. f(x+Ax)-f(x)…

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Q: How would you define f(2) in order to make f continuous at 2? limx→2 x^3-8/x^2-4 show ALL of your…

A: Let's solve limit problem.

Q: Give an example of a function that is defined for all real numbers, is continuous everywhere, but…

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Q: 28. Use the limit definition, lim 7 (x+h)- f(x) to determine the derivative of x-1. [Value of 4] h0

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Q: limit as x approaches 0+ (in the positive direction) of the function (sqrtx)^x

A: Given, f(x)= (sqrt x)^x= xx/2 = eln(x^(x/2)) = e(xln(x))/2

Q: Find the limits limx→0(ex + x)1/x

A: Consider the given limit as limx→0ex+xx

Q: Find the value k that makes the function continuous. kx f (x) = x > 9 - -7x – 7, x < 9

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Q: 2. Is the function f(x) =² continuous on the closed interval [-1, 1] ? Draw its graph illustrating…

A: Given problem:- Is the function ƒ(x) = 3/x continuous on the closed interval[−1, 1]? Draw its graph…

Q: 4) Use the Limit Definition of a derivative to find f '(3) if f(x): %3D 5-x

A: Given:- f(x) =2/(5-x)  To find:- Use limit Definition of a derivative to find f'(3)

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

A: The given curve is  f(x)= y = √(x + 2).. (1)

Q: 3) Use the limit definition of the derivative to find f' (x) if f(x) = - %3D

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Q: fox)= x+ ?

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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: Give a formula of a continuous function that is differentiable except at 0.

A: Consider the provided question, For a function to be continuous at a point x=a, we say that the same…

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

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Q: 2) Use the definition of the derivative f(x+h)-f(x) lim hー→0 to find the derivative of f(x) =…

A: Our objective is to find the derivative using definition.

Q: Find the derivative of f(x) = 1/√(x + 1) at x = 0 using the definition of the derivative as a limit.…

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Q: Calculate limit of (square root of x^2+x+1)-x as x approach to positive infinity. Thank you!

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Q: limit as x approaches infinity of (-1)x+1

A: Apply the limit.

Q: f(x)=√√x at x = 7

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Q: lim (x²Vx* – 1 – x*)

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Q: Determine the continuity of the function at the given points. forx =-1 %3D f(x = - 2, for x -1 at x…

A: If function f is continuous at x=a then limx→af(x)= f(a)