6. State the definition of the derivative of a function f. Use the definition of the derivative to In(1+x) evaluate lim if it exists. If the limit does not exist, explain why.

Q: . Does the existence and value of the limit of a function ƒ(x) as x approaches c ever depend on what…

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Q: Use the definition of the derviative to compute the derivative of f(x) = at the specific х 3.…

A: We will obtain the answer in two steps: We will simplify the difference quotient We will then…

Q: For a function f, suppose lim f(x) does not exist because the left – hand and right – hand limit…

A: Given limx→c f(x) does not exist because the left-hand and right - hand limit have different values.

Q: Use the following definition of a derivative fla=lim f\x-f(a) x-- a x-a To find fa), where f x=x°-…

A: Given, f(x)=x3-2x  To find f'(a).  Solution: f'(a)=limx→af(x)-f(a)x-a      =f(a)-f(a)a-a=00

Q: Use the limit definition of the derivative function to find 4 x2|. Which of the following is the…

A: We need to evaluate the correct step that comes just before using the direct substitution to…

Q: Estimate the limit numerically to two decimal places or state that the limit does not exist.

A: Here it is required to estimate the limit numerically to two decimal places.

Q: Use the limit definition of the derivative of the given function at the given value of x (if it…

A: Given functions are

Q: Find the limit by interpreting the expression as an appropriate derivative. In(e + Ax) – 7 (а) lim…

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Q: 1. What is the difference between a function whose limit does not exist and one that increases…

A: Definition of Limit: Let E⊆ R and f:E→R.  Let a∈R be such that ((a-r,a+r)    {a})∩E is non empty for…

Q: If a function f has no limit as x approaches c, then we say that lim f(x)

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Q: Can f(x) approach a limit as x ➔ c if f(c) is undefined? If so, give an example.

A: Yes .This statement f(x) approach a limit as x ➔ c if f(c) is undefined is correct. We will see one…

Q: 2 Use the definition of continuity to show f (x) = is x+3 continuous at x=1. Whenever you find a…

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Q: Can we evaluate the limit using f(c) if the constant c will not make the function undefined or…

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Q: Use the definition of the derviative to compute the derivative of f(x) = at the 2. Evaluate the…

A: Calculate the value for f(x) at x = (2 + h) and x = 2. Simplify the numerator.…

Q: Show that the absolute-value function y = abs(x) = |x| is NOT differentiable at x = 0. (Hint: by…

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Q: 32? And are

A: {x2                               if x<-2f(x)={x1/5                           if…

Q: For Exercise evaluate each limit by first converting each toa derivative at a particular x-value.

A: limx→-1x29-1x+1 On simplification, we get limx→-1x29-1x+1=limx→-1x29--129x--1 Now it is in the form…

Q: State the definition of the derivative of a function f. Use the definition of the derivative to…

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Q: 1. Find the derivative of f(x) = 2. at x = 0 using the definition of the derivative as a limit. Va +…

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Q: Find the limit. lim tanh(x)

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Q: express the limit as a derivative.

A: Given expression

Q: Use the definition of the derivative to evaluate the following limits.

A: Derivative of a function f(x) is defined as, f'(x)=limh→0f(x+h)-f(x)h. Derivative of a function f(x)…

Q: Use l'Hôpital's Rule to find the limit. x11X lim x→0 11* – 1

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Q: 2. Compute xe" da using a limit.

A: The given which we have to find the integration from 0 to ♾️  f(x) = xex

Q: (4) Find the limit by interpretting the limit as as an appropriate derivative. (DO NOT USE…

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Q: Which of following limits is the derivative of g(x) =5x at =2? 10 – 5h lim h 10 + 5h lim h>0 h 10 +…

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Q: Use the definition of the derivative to compute the derivative of the function f(x) : using algebra…

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Q: if f(z) = V3+ 3z, find f'(3), using the definition of derivative f'(3) is the limit as z+ of the…

A: Given query is to find the derivative using definition.

Q: By using the precise definition of the limit of a function show that lim (x,y)→(0,0) 3xy2 /(2x2+ y2…

A: If value of a function at some point is in indeterminate form then we use concept of limit to find…

Q: Show that the limit doesn't exis 3x2 1) (x,y)→(0,0) x² + y² lim 2) (х,у

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Q: Find the derivative of f(z) = at z= 0 using the definition of the derivative as a limit. Be sure to…

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Q: The L'Hospital's rule can be applied to find the limit of a function as long as you can express it…

A: L'Hospital's rule states that, the limit of the ratio of two functions is equal to the limit of the…

Q: Show work to find the derivative of the function using the limit definition of derivative. g(t) = 6t

A: solution.

Q: Compute the value of the limit below by relating the limit to the definition of a derivative of a…

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Q: e definition of the derivative (limit

A: Here we have to use definition of the derivative (limit definition) to solve the  dydxat x=2=? given…

Q: Use the definition of the limit of a function of two variables to verify the limit.

A: We have to verify the limit: limx, y→1, 0x=1 According to limit value, x, y→1, 0 therefore, x=1y=0

Q: If f(x) = 4x + 2x + 6, find f' (2), using the definition of derivative. f' (2) is the limit as x →…

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Q: 6. By considering different paths of approach, show that the following function has no limit as (x,…

A: given f(x,y)=5x2yx8+y2we need to show that the following function has no limit

Q: Given f(x) = 5VI + 1, find f'(x) using the limit definition of the derivative. f'(x)-|

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Q: Use a derivative (not L'Hospital's Rule) to evaluate (2 + h)4 – 16 lim h Enter the limit in the…

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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: Let F(x) = | 3e“ dt. Find lim F(x) if it exists. If the limit does not exist, explain why. x→0

A: see below the answer

Q: If f(x) = v4+4x, find f' (4), using the definition of derivative. f' (4) is the limit as x → of the…

A: By the definiton of limit to find f'(4) the limit of x goes to 4 and we find the limit of the…

Q: 1. Find the points at which f is discontinuous. At each of these points, state the type of…

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Q: (2+h)* Use the definition of the derivative to evaluate lim h+0 h

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Q: 1. Use the limit definition to evaluate ,(2 – 3x)dx.

A: The given integral is ∫-122-3xdx

Q: Find the limit for the following functions: x-sinx 1-lim, x-Vx² + 2x 2- lim,-o

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