a. For each of the values a = -3,–2,–1,0,1,2,3a = –3,–2,–1,0,1,2,3 determine %3D lim f(x)lim f(x) exists. If the function has a limit L at a given point, state whether or not the value of the limit using the notation ,) = m 7 (x) = L If the function does not have a limit at a given point, write a sentence to explain why.

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT Calculate the limit of the following functions at the indicated…

A: (1)  we have,  since, if we apply limit then use L-hospital rule

Q: B. Find the value of the limit. 1. lim *+1)²(x-1) x1 x³+1 x²–4 2. lim x1 x2-3x+2 x²-4 3. lim x2 x-2

A:

Q: Compute each of the following limits. Use exact values. lim y⇒8- lim y+8+ lim y 8 7y - 56 8-y 7y -…

A: is negative when . Therefore thus,    use L Hospital rule:…

Q: Find the limit for the following function, (2 + h)-1 – 2-1 lim h-0 h

A: We use to solve this limit by simplification/factorization method

Q: Question 4 Evaluate the following limits: V5x + 2x 4.1 lim Va +9-3 4.2 lim-

A:

Q: 2. Find the discontinuities, if any, for the following functions. For each discontinuity, indicate…

A:

Q: g(x) = if X²1 if X=1 2-x2 if 1≤ x ≤ 2 X-3 if x >2 X 3

A: Please see the below picture for detailed solution.

Q: Find the following limit. lim (-x² +9x-1) X-6

A:

Q: Find the limit

A: We have to find the limit of following expression: limx→55-xx2-25 First of all we need to check the…

Q: 22 - 3x – 10 Evaluate the limit: lim 4x + 8 Z-2

A:

Q: x+h-Vx 12. lim h

A:

Q: GeoGebrä Task 1: This rectangle has been decomposed along its diagonal. Recompose the two pieces to…

A: A rectangle is a closed quadrilateral with four sides and four angles. All the four angles of the…

Q: Find the lim as h approaches 0 for the given function

A: Given f(x)=x2+5limh→0f(h+4)-f(4)h

Q: Suppose that f is a function such that lim-[f(x) - 2x²]= π. Determine, if possible, lim 118 x² +1'

A: Suppose that f is a function such that, limx→∞fx-2x2=π.  To determine, limx→∞ fxx2+1, if possible.

Q: lim f(x) f(c)

A:

Q: We know the following limit expression to be true: lim (-x² + 8x-6) = 1 X-1 Choose the most direct…

A: The limit of the function f(x)= (-x2+8x-6); is 1 when x tends 1 .

Q: Evaluate the following limit: x2 – 25 lim x--5 x+5 (A) -10 B the limit does not exist + 00 D 0

A: A detailed solution is given below.

Q: Find the following limit. lim x-x 2+ x - 4x³-4 5 x³x²+1 Number

A: ans=  -4/5

Q: a. lim f(x) = %3D b. lim f(x) = %3D X-1 c. f(1) = %3D

A:

Q: 1-1/x Which of the following gives the value of lim- .? Select one: а. 2 b. .5 С. 1.5 d. 1

A:

Q: Lim é-x- つo 1+oS T-X-7

A:

Q: Evaluate each of the following limits. V2r? +1 1. lim Зх — 5

A: Explanation of the answer is as follows

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 3. Is the series n=1 2n convergent or divergent? Hint: quotient…

A: The given series is .

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.