-x ifx<0 3. Let f(x)={1-x if 01 function f. Where is f discontinuous? Justify your answer using the definition of continuity.

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

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

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: b* – 1 Show numerically that for b = 3 and b = 5, lim аppears to equal In 3 and In 5, respectively.

A: Given : limx→0bx−1x

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

A: f(x)=x3, a=-2

Q: In the given equation as follows , determine whether the statement is true or false. If it is false,…

A: f is continuous function on [0,∞) and ∫0∞f(x)dx diverges

Q: You are given that a function f is differentiable on (-o, 0), and that lim f'(x) = 6. lim (f(x + 3)…

A: Use the mean value theorem and calculate limit in following way:-

Q: O:: A- Find the limit for the following functions: - tan2x 4x-3 3x3-9x²+x-3 1- lim x→0 sin4x 2- lim…

A: A) Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Let lim,-0+ f(x) = -2, where 8r - 3 for r <0 f(x): | 4x – 2 for r2 0 f(r) = Then what is (the…

A:

Q: What is the limit as x goes to 0 for (e^x-1-x)/x^2?

A: Please refer the attached image for complete solution.

Q: Use the definition of continuity and the properties of limits to show that the function is…

A: Given function is, f(x)=(x+2x3)4, a=-1

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: What is the limit of f (x) = 1 as x → T?

A: Value of a constant function is always same irrespective of input.

Q: Let f(x) be a continuous differentiable function that f(x)- 4 satisfies lim =D5 %3D x3 x-3 Which…

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Q: Find the limit and discuss the continuity of the function.

A: Evaluate lim(x,y)→(2,4)x+yx2+1

Q: Find the value x=a where the function is discontinuous, For the point of discontinuity, give (a)…

A: f ( x ) is continuos at x = a if  * f ( a ) exist . * lim x→ a  f ( x ) exist . * lim x→a  f ( x ) =…

Q: In each case use the limit definition to compute f'(0), and then find the equation of the tangent…

A: Given: a fx=xex   b fx=x2ex

Q: Use the Squeeze Theorem to prove lim = 0. x00 x+ e- For x 0, since 0 < e* <1, we have

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Q: Which of the following graph shows that f (z) = |r - 2| is continuous but not differentiable at x =…

A:

Q: Why is the following function discontinuous at x = 1? (1+x² ifz 1 (a) f(1) does not exist. (b) lim…

A: We have to find out

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

A:

Q: given f(x) = (2x+1)/(x+3), use the limit definition to find the tangent line to graph of f(x) at x=0

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Q: (4) Find the values of a and b so that h(x) is continuous at = 4. Hint: Write down the limit…

A:

Q: 2. For the given function, f, determine if the function is discontinuous at a given point. State…

A: Function is f(x)=xx a=0 We have to check whether the function is continuous or discontinuous at…

Q: Now consider the equation for the function above: ex+2 + 4, Vx + 3 + 1, х 2 f(x) 2, 3x, Use the…

A:

Q: Find number k, so that f is continuous at every point. tan kx f(x) = x 4x+3 k2, x 20 O O and= Cannot…

A: The function is given by fx = tankxx ,x&lt;04x+3k2 ,x≥0 To evaluate : The value of k so that f is…

Q: S(x) = 7x* – 1x* +2. | Use interval notation to indicate where f is continuous. Domain of…

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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: If f(2) is a continuous function at a point z, , then f(z) is differentiable at z, . But the…

A: Authoring guidelines:…

Q: - Define the function f:R → R by ƒ (x) = x +1 if x 0 and f (0) = 4. Show that lim,-0 f (x) = 1 and f…

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Q: Find the following from the graph of the function f(x) a) lim f(x)+ S(1) = b) Is the limit f(x)…

A: Graph of the function is given, we have to find its limit

Q: Assume that f(x) is everywhere continuous and it is given to you that f(x) + 8 lim x→2 x - 2 = -4 It…

A: Consider the given expression limx→2fx+8x-2=-4 Or, -4=limx→2fx+8x-2                            …1…

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

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Q: Determine the limit as x approaches the given x-coordinate and the continuity of the function at…

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Q: (6) Draw the graph of a (a) function ƒ satisfying Y S(1) = 2, S is continuous at 1. What is lim,→1…

A: f(1)=2f is continuous at 1

Q: : A- Find the limit for the following functions: - tan2x 1- lim X-0 sintx 4x-3 2- lim x--0 Vx2+1 3-…

A: L'Hospital's rule states that for functions f and g which are differentiable in an open interval…

Q: For every continuous f:[0,+0) →R _function , if a>0 2fx'f(x*)dx =[ xf(x)dx Demonstrate that this…

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Q: Find the values of a and b such that the following function f(x) = 2a cos(x + 1) - b.5x+2, if x -1,

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Q: Find the limit of f(x) = as x approaches co and as x approaches - oo. 4 -

A: Given,          fx=-4+2x4-6x

Q: find the limit of f(x)= ((x+h)^3-x^3)/h as h approaches 0

A: SOLUTION-

Q: Find the following limits. √x-3 X-9 x-9 1. lim t²-7t+10 2. lim- t-2 t-2 3. A function f(x) satisfies…

A: Since, you have posted multiple questions, as per guidelines, we"ll solve only first three…

Q: f(x) = 3x - 5x² 1. c = 2

A: Given: fx=3x-5x2  ; c=2   The function will be continuous at x=c when, limx→c-fx=limx→c+fx=finite…

Q: Find the limit as h approaches zero of f(x)=[1/(x+h)^2-1/x^2]/h

A:

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

A: Yes, existence and value of the limit of a function f(x) as x approaches a depends on what happens…

Q: Now consider the equation for the function above: 2x + 3, x 4 - x-3 ’ 2, x = 4 Use the equation and…

A:

Q: O3: A- Find the limit for the following functions: - tan2x 4х-3 3x3-9x2+x-3 1- lim x→0 sin4x 2- lim…

A:

Q: Find the limit as x approaches infinity of the function V2 – x2 h(x) х3 — х + 1

A: Given:  h(x)=2-x2x3-x+1h(x)=x2 2x2-1x31x3-1x2+1  (Taking highest power of x in the…

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.