True or false 1. If the left- and right-hand limits of f(x) as x→ c exists and are equal,Then f(x) cannot be discontinuous at x = c?

Q: Is the limit of f (x) as x approaches c always equal to f (c)? Why or why not?

A: To prove :                   The limit of f(x) as x approaches c always equal to f(c). Answer :…

Q: Consider g(x) = x!/5. Is g(x) differentiable at x=0? Is g(x) continuous at x=0?

A: Given function

Q: 5. Show that the function h(r, y) defined by if + y 1 is discontinuous.

A:

Q: Show that the limit of the function f(x,y)= (0,0). (x+y)² x² + y² is indeterminate at

A: Limit of the function

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: true or false  if f(x) is continous at x=a, then f(x) is differentiable at x=a

A: False.    The given statement is not true in general.

Q: on f(x, y) = 3x + 9y subject to th %3D

A:

Q: If y = f(x) is an odd differentiable function defined on (-o, 0) such that %3D f'(3) = -2 then…

A: A function f(x) is said to be even if f(-x) = f(x) And odd if f(-x) = -f(x)

Q: Explain why the paths y = mx and x = y² are suitable to check if the limit of %3D xy f(x,y) = as (x,…

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Q: If f(x) is differentiable at X =c then lim f(x) must exist and f(c) must be defined

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Q: Suppose F 1  and F 2 are both antiderivatives of f on an interval I How are  F 1  and F 2  related?

A: Given:  F 1  and F 2 are both antiderivatives of f on an interval I. That is,

Q: If f(x) is continuous at x = c then f'(c) exists. True False

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Q: If functions ƒ(x) and g(x) are continuous for

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Q: Let y = f(x) be a continuous function. If ƒ has a local maximum or minimum value at x = a, then the…

A: Let y=f(x) be a continuous function. If f has a local maximum or minimum at x=a,then the limit…

Q: Answer the following True or False: If f(x) is a differentiable function such that f'( – 2) = 0,…

A: Given  f(x) is differential function  f'(-2)= 0   means x= -2 is critical point of f(x)

Q: Is it true or false: that a two sided limit of f(x) as x approches c exist if the value of f(c) does…

A: The statement is given as a two sided limit of f (x) as x approaches c exist if the value of f (c)…

Q: Let g (x) = f' (x) be a continuous function. If the derivative of the continuous function g (x)…

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Q: If f"(c)<0, where c is a critical value and f(x) is a continuous function over an open interval I…

A: We have to find f(c)

Q: Suppose f is continuous on [0, 1]. What is lim n→ ∞ 1 S fo 0 f(x) dx?

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Q: Show that the absolute-value function y = t(x) = |x − 5| is NOT differentiable at x = 5. (Hint: by…

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Q: Suppose that f and g are discontinuous at x = c. Does it follow that f + g is discontinuous at x =…

A: Let us define that Then both f and g are discontinuous at x=2

Q: Evaluate , x? dx by limit definition. f(x) dx f(G.) Ax¡ lim i=1

A: Given integral  ∫01x2dx △x=b-an△x=1-0n=1n ci=a+i(△x)ci=0+i1nci= inf(ci)=in2

Q: . Explain why f (x) = sin (x² + 3r + 1) is a continuous function for all c eR.

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Q: Let f(x) = 3x² – 5x + 1 f(x+h)-f(x) (a) Find f'(x) using the limit definition of derivative. That…

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Q: True or false? The limit of 1/x as x approaches zero is zero.

A: The given statement is false. Use the property of limits to solve the limit.…

Q: Show that the limit of the function f(x,y) = at (0,0) does not exist. (x+y)² x² + y²

A: Limit of a Function: Like a single-variable function, a multi-variable function can also have limit.…

Q: If f(x) =0 at x=c then f has either a minimum or maximum at x=c. If a differentiable function f has…

A: To Determine: true or false                           1) if f'(x)=0 at x=c then f has either a…

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: Given the function f(x) = x² – 2x, what is equation of the tangent line to the graph of f at x = -1?…

A: 1. f(x)=x2-2x at x=-12. f(x) and g(x) are differentiable functions, f'(x)=3x and g'(x)=2x23.…

Q: 3. Show that x? if x>0 0 if x<0 f(x) = is differentiable at xo =0 but f' is not differentiable at xo…

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Q: 3. True/False: if the limit of a function exists at x=c, then f(c) exists.

A: The given statement is

Q: that makes y continuous but not differentiable by writing the required procedures to that If: X≥0…

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Q: 7. Find the limit as x approaches 0. F V I 2 2 O infinity O limit does not exist Oo .

A:

Q: b) Show that the function f (x) = { * x² sin ! for x E (0, 1] for x = 0 is absolutely continuous on…

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

A: fx=1,  x≠20,  x=2

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

A:

Q: . Apply the two path test to make sure the following limit exist or not at (0,0) xy f(x, y) x³ +…

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Q: 1-cost lim sint et-1 + t t t+0

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Q: a) Evaluate in terms of Gamma function ∫e^(−y^2) y^13 dy   limit 0 to ∞ b) Find ∫f(x) dx limit: 1…

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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: Show that f (x, y) = has no limit as (x, y)→(0,0) Vx2+y2

A: The objective is to show that f(x,y) has no limit as (x,y) approaches to (0,0).

Q: TRUE or FALSE. If f is undefined at x = c, then the limit of f (x) as x approaches c does not exist.

A: Given statement If f is undefined at x=c, then the limit of f(x) as x approaches c does not exist.

Q: Show that f(x) := x/3, x e R, is not differentiable at x 0.

A:

Q: Prove: f(x)=5x y is continuous at x=2

A: A function fx is continuous at a point x=a, if limx→afx=fa Given function is

Q: 1 if z 0. Is F(x) is continuous at I = 0? Justify your answer.

A: Given that for x&lt;=0, F(x) = (x - 1)/4 Then as x tends to zero from the negative side of zero, we…

Q: what is the limit of f(t) as t approaches 3. F(t)= ((1/t)-1/3)/t-3?

A:

Q: Suppose that f(x) is a continuous function on the interval [0, T] . If f(x)=(sin x)ª for 0<x<T, then…

A: we have to find the value of given function. the solution is following.

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.