Evaluate the following limits: (a) lim (x² + x) (3x³ + 6) x-2 (b) lim vu² + 3u + 6 u--2 2x + 12 (c) Let f (x) = |x+ 6| Determine: (i) lim f (x) x-6+ (ii) lim ƒ (x) x-6- (iii) Use (i) and (ii) to deduce lim f (x) at x = 6.

Q: Evaluate the limit of the function: lim f(x) =- /7 +x -V7

A: topic - limits

Q: Find the limits lim х2 — 1 as a. x→1+ b. x→1 c. x→-1+ d. x→-1

A: we have to find the limit    the given expression is

Q: Find the limit V3x(x-1) lim→1 |x-1|

A: we have limx→1-3x(x-1)|x-1| this is 00 indeterminate term

Q: Evaluate the limit. x² +3x - 10 lim-5 2x + 10

A:

Q: 3x -4x b) lim X→-00 x2-2x3

A:

Q: Evaluate the Polloung limits ad lim メ→ 0 Ilx³– 2x²~ 9 x 3 - 10x - 8 x3 ) lim メS-0 Ilx³- 2x²- 9 x –…

A: We havelimx→∞11x3−2x2−9x3−10x−8x3Multiply and divide by…

Q: Find the limits lim (V² + 3 + x) X -00

A:

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: Find the limits a) lim x2 - 4x + 3 x2 - 1 when x approaches 1 b) lim 6x + 100 7x2 100 when x…

A: We have to find the limit

Q: Find limit (a) by investigating values of the function near the point where the limit is taken and…

A: Given that, limx→1x4+2x3+2x2-10x+5x2-1 Consider f(x)=x4+2x3+2x2-10x+5x2-1

Q: Find the limit (if it exist).

A: Given,

Q: Find a Limit using factoring:

A: We have to find the limit using factoring: limx→1x2+2x-3x-1 This is 00 indeterminate form of limit.…

Q: Evaluate the fo llowing limits lim x8 + 7x + 9x-4x² +2 Xヨ-0 x4 - 4 y5 - 3x*-6x +4 2x2-8x +7 suppose…

A: 1) To evaluate:  limx→-∞x8+7x6+9x5-4x2+2x4-4x5-3x2-6x+4 Dividing numerator and denominator by x4, we…

Q: Find the limit.

A: Given  The limit is limx→02+x-2x.

Q: Find the limit of the function lim x → − 6 ( 2 x + 12 | x + 6 | )

A: Find the limit

Q: Find the indicated limit. 2x lim (- Vx2+1 X00

A: Find the indicated limitlimx→∞(2xx2+1)

Q: x² + x lim * + 2x + x³

A:

Q: Evaluate the limit x2 + 8x + 15 lim x → - 3 x + 3

A: =?

Q: Evaluate the limit: -V4+x² lim X→0- x2

A: limx→0--4+x2x2

Q: Estimate the value of lim 1 + 3x 1 by graphing the function f(x) = x/(/I + 3x – 1).

A: It is given that limx→0x1+3x-1 It is known that if we have limx→af(x)g(x), and after plugging the…

Q: Find the limit. . lim 2x²-x-3 X-1 x+1 . lim 2+h-vZ x-5 E lim x-5+ x2-25 . lim o. f (x) = fx³ +3 lx -…

A:

Q: Lim X-0 √1+x-√1-x x

A: evaluate the limit limx→01+x-1-xx

Q: Find the limit of the function lim x² 3x +2 X-1 X-A

A:

Q: What is lim )-7(0) if f(x) = 2x2 + 1? x-0 The limit does not exist. 1

A: Solve for the limit

Q: Find the limit if it exists. Vx - 5 lim X х- 25 X 25

A: Find the following limit

Q: what is the lim x->0  f(x)-f(0)/x^2 if f(x)=2x^2+1?

A:

Q: Use the graph to evaluate the limit. 3) lim f(x) x-0 3) 3+ 2+ 4 X 4) lim f(x) x-0 4) 3+ 10 -4 -3 -2

A: Graph of the function is given, we have to find its limit at x=0

Q: Evaluate the limit: x² - 7x + 3 lim x→∞ x3 - 9x2 + 2

A:

Q: Calculate the limit algebraically: x³ + 8 lim x→-2 x² + 7x + 10

A: Consider the given expression, If we substitute  in the expression we get  form. so, use L-hospital…

Q: V x2 + 9 - 5 lim X→-4 x + 4

A:

Q: Find the limit of lim((9+3x)1/2-3)/x as x approaches 0

A: To determine the value of the limit.

Q: a) lim 3x2-10x5

A: Find the limit of 3x^2-10x^5 at - infinity

Q: Find the limits algebraically: (a) lim vx2 + 2x – 3 x-3

A: Find the limit of the given expression. Given function is continuous at x=3. So we can apply the…

Q: 4x 3. lim X-4+Vx-4

A:

Q: Find the limit. -7x + 5 lim Vx2 + x X→-0

A: Given limit, limx→-∞-7x+5x2+x

Q: (b) Given that lim f(x)== 2 and lim g(x) =4 , find the limit x→2 x→2 1 lim 3f(x)- Vg(x) x→2 Using…

A:

Q: Find the limit. y 6- 5- 4 3- 2 1- 3-2 -1 -1 1\2 3 4 5 -2t limz-0 f (x)

A:

Q: Evaluate the limit. 4x2-9 lim x→3/2 15-10x а. b. lim(x – 2) sec(n/x) | x-2

A: See the details solution in below

Q: If lim (x approaches 6) (f(x)-4)/(x-3)= 2, how do I find lim (x approaches 6) f(x)?

A: We separate the limit first.

Q: Find the limit. Vx +7-4 lim X-3 X-3

A: limx→3 x2+7-4x-3

Q: Find the limit x-5 lim x→5 x²-25

A:

Q: Find the limit. x² - 25 lim x 5 x²8x + 15

A: We need to find the limit:limx→5x2-25x2-8x+25

Q: Find the limit. /x² +3 - 2 lim X- 1 X1

A:

Q: Q1 find the limit x' -1 lim x –1

A:

Q: Find the following limits. x²+3x-4 x -16 1. lim 2. lim X-1 X-1 x+2

A: Apply the limit to the given expression and if it results in 0/0 form then take the derivative of…

Q: 2/ Find the limit of the function lim X415 хъ Ч 2 X

A:

Q: Determine a reasonable estimate for lim hx x-1 3 -5 -4 -3 -1 3 5 2. 1 4. 1. 1. 2. ee

A:

Q: Evaluate the limit. x2 + 2x – 15 lim- x – 3 X-3

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.