x² + 3 for x < 1 for 1 2 f (x) = { 10 – x y у 3 10 — х y = 6x – x² y = x² + 3 1 2 6

Q: Complete the table by computing f(x) at the given values of x. x2 + 5x – 24 f(x) = X - 3 2.9 2.99…

A: From the given function: fx=x2+5x-24x-3 So, At x=2.9 f(2.9)=2.92+52.9-242.9-3=10.9 At 2.99…

Q: Let f(r) = -2 and let g be the function defined by %3D (x – 3)(r – 5) if a 3 (a) Evaluate lim (f…

A: Function f(x)=-2x  and g(x)=(x-3)(x-5)if x&lt;33x-x2if x≥3 To evaluate limx→3(f∘g)(x)

Q: Let f(x) = -2 and let g be the function defined by (x – 3)(r – 5) if r 3 (a) Evaluate lim(f o…

A:

Q: Which of the following limits represents f '(2) if f(x) = 2x + 3 O A. 2(2+h)´ +3-11 lim h→0 OB. (2x…

A: To check the limit representation of f’(2) of given function.

Q: Use the table of values to find the limit, if it exists. If it does not, enter "DNE". x (from the…

A: Function value from the left and right of the 5 is given.

Q: 3. Use the definition of continuity and the properties of limits to show that the function is…

A:

Q: Let f(x) = – and let g be the function defined by (x – 3)(x – 5) if x 3 (a) Evaluate lim(ƒ o g)(x).…

A: Ans:-  a) - infinity  b) infinite discontinuity  Explanations:- In part (b) as LHL is not equal to…

Q: Sketch the graph of the function f. (x - 6 -{-2x + 3 if x s 3 if x > 3 f(x) = y 1아 1아 5 -10 -5 10…

A: Since you have answered the first question correctly, I'll solve the next question. We first find…

Q: 1. Let f(x) = 5x². Show that f(3 + h) = 5h? + 30h + 45. Then show that f (3 + h) – f(3) = 5h + 30…

A:

Q: (-3,0) 3 -2 4- 3+ 2. -1 (0, -0.5) -1,-2) (-1,-3) -3- (1,0) 2 y = f'(x) 3 (2,-0.5) (3,-2) (4, -3) I

A:

Q: Sketch the graph of the following function and use it to determine the following limits. If a limit…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Consider the following function. 1 f(x): X + 9 Find the limit. lim Ax→ 0 f(x + Ax) - f(x) Ax

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Q: Suppose that f (x) = 1 if æ 1; and that f(0) = 0. Assume that f(x) isn't defined on [-1,0) U (0,…

A: It is given that fx=1x≤-1fx=1x≥1fx=0x=0. Sketch the graph as follows:

Q: Compute the limit as xà0 of f(x)=[(9+x)^(1/2)-3]/x, if possible.

A:

Q: Suppose that f(f) and f(t) are defined for all t and that lim, t f(1) = -7 and lim, , g(f) = 0. Find…

A: Given:         limt→t0f(t)=−7  and  limt→t0g(t)=0.

Q: Sketch a graph of the function and answer the following limit questions about it. т (т) т 2 where m…

A:

Q: Suppose the functions f(x) and g(x) are defined for all x and that lim,0 f(x) = 1/2 and lim, o 8(x)…

A: Given:            limx→\0f(x)=12  and limx→\0g(x)=2

Q: Let f(x) = x^100 e^-x   (A) Find a lower bound for f(x) for x > 0. In other words, find a number m…

A: Given a function, fx=x100e-x. (A) To determine a lower bound of fx for, x&gt;0. For, x=1, f1=1e As x…

Q: Suppose that for a function f, f(3) is not defined. Also suppose that lim f(x) = 2 and lim f(x) = 2…

A:

Q: Suppose that f(f) and f(t) are defined for all t and that lim, f(t) = -7 and lim, h 8(1) = 0. Find…

A: Given: limt→t0cosgt

Q: Consider the function f(x) = x +7x. Which one of the following limits represents f'(1)? f(1+ h)-f(1)…

A: Definition: Let f be a function and a be a point in its domain. the function f is said to be…

Q: A function f is defined as follows: (px2 – 4, = {2x – 1, x 5 8-x., (a) Given that the limit at x = 3…

A:

Q: Sketch the graph of the following function and use it to determine the following limits. If a limit…

A: To sketch the graph of given function and find the limits

Q: consider the function g(x) =   2 − πx         if x ≤ a               x^4              if x > a…

A: We are given the following function. We need to find a value of a. Idea: We will find the value of…

Q: 1. Compute the following limit Væ2 +1–1 lim Hint: Note this function is not defined at x = 0. But…

A: To evaluate the given limit

Q: Let f(x) = and let g be the function defined by %3D (x – 3)(x – 5) if x 3 () Evaluate li (b) Is ƒ…

A: We have to find

Q: Let ƒ : D → R be a function and let xo be a limit point of D that also belongs to D. Show that the…

A:

Q: Suppose f′(x) is continuous with f(9)=8 and f'(9)=-12. Calculate the following limit or determine…

A: Answer and explanation is given below

Q: Consider the following. [2 x -1 if x 1 Is f differentiable at x=1 ? Yes, because f is continuous at…

A:

Q: #2: Consider the function f (x) = X*9 and the limit lim f(x). X→1 (a) Find the maximum value of ô…

A: The given function f(x)=x+95and the limit limx→1f(x)

Q: 1. Consider the function given by if r € QU [0, 1] f(x) = 1- I 1 ° if r E Q°U [0, 1] Determine if…

A:

Q: If function f(x) and g(x) are continuous everywhere and f(1)=2, f(3)= -4, f(4)=8, g(0)=4, g(3)= -6,…

A:

Q: If the limit of f(x) as x approaches cis 0, then there must exist a number k such that f(k) < 0.001.…

A: Explanation: If limx→cf(x)=0, the for any positive ∈, (Like 0.001) there is a positive δ such that…

Q: Let f(x) = 5 + 9x -9. According to the definition, f'(x) = lim (Enter the limit in reduced form) h 0

A:

Q: to this answer. Evaluate the left-hand limit of as f (x) = x8. 16-2x O 1/2 O -1/2 O undefined

A:

Q: Given the table of values of the function below, what is its limit as x approaches -1? x -1.25…

A:

Q: #2: Consider the function f(x) = and the limit lim f(x). x + %3D x→1 (a) Find the maximum value of d…

A: see below the answer

Q: Suppose the functions ƒ(x) and g(x) are defined for all x and that

A: Dear student, since you have posted multiple sub parts, as per our policy we will answer first three…

Q: Let f(x) = and let g be the function defined by (x – 3)(x – 5) if x 3 valuate lim (f o g)(x). fog…

A:

Q: 8) Suppose if r 20 if r < 0. f(r) = Identify a function g with domain R such that lim(f+g)(x) exists…

A: The explanation is as below

Q: Let                        gn(x)=nx + x2/ 2n, and set g(x) = lim gn(x). Show that g is…

A: Given: gn(x)=nx+x22n   and  setting  limn→∞ gn(x)=g(x)Now,…

Q: 3. Use the definition of continuity and the properties of limits to show that the function is…

A: As per our guidelines we are supposed to answer only one question i.e. the question no (a). For the…

Q: Recall that a function f(x) is continuous at a value x = a if 1. the limit of f(x) as x approaches a…

A: Given piecewise function f(x)=x+k   , if x&lt;-5x2 , if  x≥-5

Q: 4. Evaluate the following based on the given graph of f(x). 31 -4 3 -2 -1 2 3 -1 -2 -3 a) lim, e.)…

A:

Q: Consider the equation below, what is the value of the limit of f(x) as x approaches a, if f has…

A: We are going to find limit at x= 0 and x= -1

Q: Consider the following function. f(x) = 8x2 – 8x Find the limit. f (r + Ax) – f (x) lim Ar-0 Ar

A:

Q: Let f be the function Зх + 5 for x 5 х Compute the left- and right-hand limits at x = 5 and…

A: Now, Left hand limit at x = 5 is, And right hand limit is,

Q: Sketch the graph of the following function and use it to define the following limits, or specify if…

A: As per norms, the first three questions are answered.

Q: Let f : D → R be a function and let xo be a limit point of D that also belongs to D. Show that the…

A:

Q: x5 – x4 – 2x3 - f(x) = x4 – 3x3 – x2 + 3x O and infinity O and -3/8 -3/8 andinfinity O O and 3/8

A: The given function is  fx=x5-x4-2x3x4-3x3-x2+3x A function f(x) has removable discontinuity at x=a…

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.