4. Find the following limits or determine that they do not exist: 1+1/x a. lim,-0 1+1/x² 1+1/x? b. lim,→0 1+1/x 1+1/(x – 1) c. lim→1 2+1/(x – 1)-

Q: [x2+3x-1 a. lim 1 6 b. lim X+2 Lx-2 x2+2x-8 E. lim - h-0 h x+h Vx+h-Vx d. lim x >0 h-0 h

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

Q: 1. lim (x – 4)(x² + 8) x→5 2(t-10)² 2. lim t→10 t

A: Let P(x) = a0+a1x+a2x2+.....+anxn be a polynomial, where a0, a1, ...., an are real numbers and n is…

Q: Apply the Gram-Schmidt Process to the basis B to obtain an orthogonal basis for the inner product…

A: The given basis are B=1, 1+x, 1+x+x2 on the vector space V=P2ℝ. We have to find the orthogonal basis…

Q: 2 3 ( - 1²/1 ) ² 3 lim 3 X→∞ x

A:

Q: 7x If h(x) = (1 + 4)¹x, find lim h(x) X→∞

A: In the question is :h(x)=1+4x7xlimx→∞hx=limx→∞1+4x7x

Q: lim X+ X+)X +3 2x-X-1

A: Given: The function is  f(x)=x3+x2+x+32x3-x-1   To determine: limx→1x3+x2+x+32x3-x-1

Q: Consider x = 3x1 – 2x2, x, = 2x1 – 2x2, with x (0) = 3, x2 (0) = ;. b If x1 ge + e-, find the values…

A:

Q: 7x f h(x) = (1 + 4) ¹*, find lim h(x). X→∞

A: Please see the below picture for detailed solution.

Q: 2x lim x→9- 4-/25-x

A: This question is related to limits, we will solve it using given information.

Q: Evaluate lim (1+x)/x x→0

A: Please see the answer in step 2

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

A: Above question is solved.

Q: 6. Calculate limit: lim tg x X→0 2-V4+3x

A: Here we have to calculate Limit =limx→0 tgx2-4+3x

Q: Which of the following limits can be evaluated using L'Hôpital's Rule? Зх- 12 A.lim x→4 x2 +16 Зx-12…

A:

Q: 10. Use the definition of limit to show that a. lim (x² + 4x) = 12, Z-2

A:

Q: x+h-Vx 12. lim h

A:

Q: Find the limit limx→∞(1+1x)3x.

A: we have to find the limit : limx→∞(1+x)(3x)

Q: 9x¹+x x-100 2x¹45x²-x+6 iv. lim

A: Given limx→∞ 9x4+x2x4+5x2-x+6

Q: limits

A: L'Hospital's rule apply only when there is 0/0 for ∞/∞ form.

Q: If 3x − 1 ≤ f(x) ≤ x2 − 3x + 8 for x ≥ 0, find lim x→3 f(x).

A: Here we use sandwich theorem Also known as squeeze theoremThis theorem states that , if gx≤fx≤hx in…

Q: Find the value of a so that √x²-5x = 4 Vx2 lim √x² + ax - X18

A: We are required to find the value of a for which limx→∞x2+ax-x2-5x=4

Q: x²-4 lim x-2 (x-2)² 2–4

A:

Q: 3x lim х-2 V4х+1-1 4x+1

A: We can find the limit as below

Q: 3. Evaluate the following limits, if they exist: 1 (a) lim 1 +3 2x x→-0

A:

Q: Evaluate: 1. lim [√x² + x − √x² + 4] = X→ +∞ 2. lim [(x²-In(x + 1)) cotx] -0-x

A:

Q: If f(x) = 2[g (x)]³+7, then what is f'(x)? (A) f'(x)=6g (x) g'(x) (B) f'(x)=6g'(x)…

A: Use the chain rule of differentiation and then solve .   As per the bartleby guidelines I am allowed…

Q: Q5. Evaluate the limit Vx+h- Vx lim h-0 Vx+h+Vx in the two cases (i) x > 0 and (ii) x = 0.

A: Evaluating:                                    limh→0x+h-xx+h+x   In the cases:…

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.