Evaluate the following limit.

Q: sun(log(1+z)) 230Log(1+ Suin2) um 2-)0 log(i+sinx)

A: We will use the result  If limx→af(x)g(x) = 00 , then limx→af(x)g(x) = limx→af'(x)g'(x)

Q: 2x*y lim (л, у) -> (0,0) х8 + 6у2 6y2

A:

Q: √6 + 2x² lim x→∞ 6 + 10x [ZX][][+] [94] lim x-→-8 6 + 10x || ||

A:

Q: С. 6x° – 12x +13x³ - 5x +7 1. lim 14x7 -13x +1 1x³ + 4x? – 6 15x8 – 13x +9x6 – 5x³ + 4 - 2. lim 13x°…

A: 1.  Given: To evaluate the given infinite limitslimx→∞ 6x8-12x5+13x3-5x+714x7-13x4+11x3+4x2-6=limx→∞…

Q: lim x².e 2.

A: The given limit is in the indeterminate form, just using L,Hospital's rule and easily find the…

Q: 10x? .2 +11гу + у? lim (л,у) —(-1,10) 10а2 — 39ху — 4y2

A:

Q: 1-х? а.) lim (x– 1)? Зх-10х3 b.) lim 5x - 7x? +1

A: (a) Given information: limx→1-1-x2x-12 To determine the limits first simplify,…

Q: a) lim- 1 3x +x+1 -x +5x b) lim f(x) where f(x)={ (4x xs2 3x x>2 sin 2x c) lim g(x) where 2+x < g(x)…

A: alimx→∞−x2+5x3x2+x+1Divide and multiply by x2limx→∞x2−x2+5xx2x23x2+x+1x2limx→∞−1+5x3+1x+1x2=−13

Q: sin limy→0 e

A:

Q: (3-12г (a) lim,→+∞ ( 3r+5 + csc 4x (b) lim,¬0 sin r-x² 2x (c) lim,¬∞ sec 4x+5 (d) lim,-0 1-cos r-x²…

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

Q: Evaluate the following limits.

A: We have to evaluate the limit: limx→0ax-bxx It is 00 form. We know the formula, limx→0ax-1x=lna So…

Q: Evaluate the following limits.

A:

Q: following

A: Given, limx→ 0sinx-x+x36x5

Q: Xy + yz + z lim (x,y,z)→(0,0,0) x² + y² + z²

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.