5. Let a, b, and c be real numbers with a < c< b and let f : (a, b) → R be a monotone function. If c is a point of discontinuity of f, prove that lim f(x) # lim f(x).

Q: 1 lim x x→0

A:

Q: 1. Let f(x)= x²+x-6 |x2| 7 x b 2 x + a 3 2 if x 2

A:

Q: 5. Evaluate each expression using the given graph of f(x). lim f(x) a) x-1- 2- 1- b) lim f(x) -2 -1…

A: Given graph, The objective is to find,  a) limx→1-f(x)  b) limx→1+f(x)  c) limx→1f(x) d) f1 e)…

Q: 3 Use the Squeeze Theorem to evaluate lim f(x), where f(x)=x²cos (-). x A B C D - 0 0 1 8 -0-x

A:

Q: 6. Consider a function f with the following property: if g is any function for which lim g(x) does…

A: One side is not true i have given the contradiction.

Q: 1. Complete the following based on the graph of f(x). 0 10-8-6-4-2 CO 6 4 2 2 -4 क -8. f(x) e 246 6…

A:

Q: which of the following statements is true about the function             3x-2, if x&lt;2 r(x)=…

A: We have given,            3x-2, if x&lt;2r(x)=     -8      if x=-2             5x+4 if x&gt;2

Q: 5. Let a, b, and c be real numbers with a <c<b and let f: (a, b) point of discontinuity of f, prove…

A:

Q: 2x +1 if x3 (А) -5 в) 6 23 D) -13

A: Here I am attaching image so that you understand each and every step.

Q: Let f and g be real functions. Show directly from the definitions that if f is everywhere continuous…

A:

Q: X 2 +2 x-2 3. Find lim 4. Prove that lim(2x² +1)=3

A: Dear student,                       According to our guidelines we are supposed to answer only first…

Q: Determine the right- and left-sided limits of the following function: lim x-3- (x + 1) lim x-3+x - 3

A:

Q: If-x-2+5 ≤ g(x) ≤ |x − 2|+5 for 1 ≤ x ≤ 3, evaluate lim, 29(x). Provide your answer below: lim g(x)…

A: Given,  then we have to evaluate

Q: Prove positive function so that lim + (x)=16, then lim√(x)=4 directly from definition that it f is a…

A: Given that Let  f is a positive function so that  limx→-4f(x)=16  .

Q: Find the lim tan ( X-0

A:

Q: b) Evaluate lim g(x) if 2x − 1 ≤ g(x) ≤ x² − 2x + 3 x→2

A: Above question is solved.

Q: 2- Determine lim[ v( x-1000)+10]/x x-0

A: Given problem:-

Q: Find the lim f(x) if, for all x > 13, 7x – 3 < fx) < 7x² + 4x

A: Given : 7x-3x &lt; fx &lt; 7x2+4xx2

Q: 2 lim_x(x²) +0+x

A:

Q: Let f be entire and suppose that lim 80+z f(z) Z = 0. Show that f is constant.

A: The given problem is to show that if limz→∞f(z)/z = 0 for the entire function f(z), then f(z) is…

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: Find. 1) a. lim f(x) and b. lim f(x). 3- 4-

A: Answer and explanation is given below..

Q: Evaluate using the identity a3-b3 = (a-b)(a2+ab+b2)

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 limit lim x →∞ 8x³3x² - 6x 11 - 11x - 6x³

A: Solve for the limit

Q: Use the definition of limit of a function to findlim x3 −3x−2. x→2 x2 −3x+2

A: Limit x tending to 2 = 9.Explanation:Step 1: Step 2: Step 3: Step 4:

Q: If lim fx) - 7 x-1 x - 1 5, evaluate lim f(x). X-1

A:

Q: Evaluate the limit: lim 3z4 – 8z = - %3D Z - 1

A:

Q: If f is C2 on an interval prove that f(2 + k) – 2/(2) + {(z =A) = r"(2). - lim h-0 h2 = f"(x). The…

A:

Q: 1² – 1 - 1 lim +1- a? – 2x +1'

A: To

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.