g(x) = 1/(2x), c = 1/4

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line.

A: Answer: f'(-2)=-1

Q: use the formal definition of limit to prove that the function is continuous at c. g(x) = 1/(2x), c =…

A:

Q: compute f ' (a) using the limit definition and find an equation of the tangent line to the graph of…

A: Plug x=4 to find f'(4) Answer: f'(a)= -1/16

Q: Let f (x) = xex . Use the limit definition to compute f'(0), and find the equation of the tangent…

A: Given: fx=xex We know that f'x=limh→0fx+h-fxh…

Q: compute f ' (a) using the limit definition and find an equation of the tangent line to the graph of…

A: Given f(x)=x2-x The limit definition for derivative of a function is given as: Using the above…

Q: Let f(x) = V13 – x. Compute f'(4) using the limit definition f'(4) =| Find an equation of the…

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Q: Show that the function f(x, y) x4 + y? has no limit as (x, y) approaches (0,0).

A: Note: Since we can solve at most one problem at a time, we have solved the first one. Kindly…

Q: Express the limit as a definite integral on the giveninterval.

A:

Q: use the formal definition of limit to prove that thefunction is continuous at c.

A: Given: hx=2x-3 To Find: To prove that the given function is continuous at c=2

Q: Fill in each blank so that the resulting statement is true.

A: We know that the derivative of f at x, denoted by f'x, is defined by limh→0fx+h-fxh provided that…

Q: use the limit definition to compute f'(a) and find an equation of the tangent line. f (x) = x3 + x,…

A: For a function f(x) the limit definition for derivative at x=a is f'(a)=limh→0f(a+h)-f(a)h. The…

Q: If ƒ is differentiable at a, must ƒ be continuous at a?

A: we know that for a given function if it is differentiable at given point then it must be continuous…

Q: Evaluate f x2 dx using the limit defintion of the definite integral.

A:

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line. f (x) = x3 + x,…

A: Anwer: f'(0)=1

Q: Suppose that  ff"' is continuous and f'(c)  =f"(c) =0 , but f"'(c) >0. Does f have a local…

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Q: Use the limit definition to compute f 1 (a) and find an equation of the tangent line. f(x) = 2x 2 +…

A: Given:                fx=2x2+10x,     a=3 Find: f3+h and f3 f3+h=23+h2+103+h…

Q: use the formal definition of limit to prove that thefunction is continuous at c.

A: To prove that f(x) is continuous at x=1, we have to show that limx→1 f(x)=f(1). Now  f(1)=12-7=-6.…

Q: define the function at 5 so that it becomes continuous at 5.

A: First, we rationalize the function, so that it becomes continuous at 5 which is shown on the board

Q: use the formal definition of limit to prove that thefunction is continuous at c. F(x) = √,9 - x, c =…

A: Given: Fx=9-x, c=5 we know that any functionfx is continuous at given point x=c if,…

Q: Use the limit definition to compute f 1 (a) and find an equation of the tangent line. f (x) = x +…

A: For a function f(x) the limit definition for derivative at x=a is f'(a)=limh→0f(a+h)-f(a)h. For a…

Q: Use limits to determine if f(x) = 1 is continuous at x = 0. (z+2)?

A:

Q: Express the limit as a definite integral. [Hint: Consider f(x) = x".] lim 5 i = 1 1 dx

A: To express the limit as a definite integral, limn→∞∑i=1n3i4n5

Q: Use the definition of continuity to determine whether f is continuous at a.

A: Solution:Given     f(x)=x-4if x≤0x2+x-4if x>0and a=0To find :f is continuous at 'a'Formula:limx→a…

Q: compute f'(a) using the limit definition and find an equation of the tangent line to the graph of f…

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Q: use the formal definition of limit to prove that thefunction is continuous at c. h(x) = √,2x - 3, c…

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Q: Use the limit definition to compute f 1 (a) and find an equation of the tangent line. f (t) = 2…

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Q: Let f(x) = /20 – x. Compute f'(4) using the limit definition f'(4) - - Find an equation of the…

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Q: If ƒ' is continuous on [0, ∞) and lim→∞ f(x) = 0, show that I p'(x) dx = = -f(0)

A: First we will integrate then put limit

Q: use the formal definition of limit to prove that the function is continuous at c. h(x) = sqrt(2x -…

A: To show that the function is continuous at x=2 we will find the left and right-hand limit at x=2.

Q: show that f,given by f(x) x +0 )is continuous on R-{0}

A:

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line.

A: Answer: f'(a)= 3sqrt(10)/10

Q: Find the limit of f(x) as x approaches 2, where

A: fx=1,  x≠20,  x=2

Q: if x = 0 f (x) = %3D x* sin(-) otherwise

A: In the given question, concept of continuity is applicable. Continuity Continuity for a graph y=fx…

Q: Use limits to determine if f(x) = is continuous at x = 1. z-2

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Q: Express the limit as a definite integral. [Hint: Consider f(x) = x2.] lim i = 1 n' xp 1.

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Q: Use the definition of the integral to write sec x dx as a limit. Do not evaluate the limit.

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Q: 1 lim x sin x x2 x→0 O 1/5 O 1/7 О 16

A: Given, limx→01x sinx-1x2

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line.

A:

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line. f (x) = x−1, a…

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Q: If f(z) is continuous at z then it must be differenttiable at z, 0.

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Q: . Is f(x)= Vx + 1 continuous at x == -1? Yes, because all functions are continuous No, because the…

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Q: Express the limit as a definite integral on the given interval. lim x, In(2 + x^)Ax, [3, 4] n- 00

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Q: Let f(x)=√18 x. Compute f'(2) using the limit definition f'(2) = Find an equation of the tangent…

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Q: Let f (x) = xex . Use the limit definition to compute f ,(0), and find the equation of the tangent…

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Q: d. Use the limit definition of the derivative, f (x) = lim f (x+h)-f(x) 1 +h)=j, to prove that VT =…

A:

Q: If f' is continuous on [0, ∞) and limx→∞ f (x) = 0 , showthat

A: Given, If f' is continuous on the interval [0,∞) and limx→∞f(x)=0 show that, ∫0∞f'(x)dx=-f(0)

Q: Let f(x) = v58 – x. Compute f'(9) using the limit definition f'(9) = Find an equation of the tangent…

A: We have to find

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.