(a) Using only the definition, show that lim xx0x2

Q: evaluate the following limits (1 + x): -e lim-

A:

Q: Show that

A: We have to show that: limx→∞1x=0 We know that 1∞=010=∞

Q: Consider the following lim -1 1+

A: To determine the given limit, first apply the limit, as follows; limx→0+(1+1x)x=1+100 =(∞)0   which…

Q: Evaluate e2x – 1 lim- X

A:

Q: b ax + x2 Evaluate lim where a>0

A: Limit of given function is solved.

Q: 1. Evaluate. a) lim b) lim x² + 9x-4 x²2x-8 x + 2

A: The solution is shown in step-2

Q: Find the limits in Exercise

A: limx→-2xx+12x+5x2+x

Q: lim X(In x)2 requires repeated application of L'Hopital's rule. Show all the steps.

A:

Q: let fcx)-x2+てメー1X, five a) limf(x) メ -7 O b) lim f(x) Xー70

A:

Q: Evaluate the dim Y-3 8-9

A: Let  f(x) is a well defined function of x then for constant a and l  , as x approaches to a f(x)…

Q: 5z 3z (a) Evaluate lim, >00 94e

A:

Q: lim x-00 x2 –10x+3

A:

Q: x²-3x-10 a) lim x-5 x-5

A:

Q: explain why the entire real line R is both open and closed.

A: In standard topology, the entire real line (R) is considered both open and closed. Let's break down…

Q: Find the one-sided limit

A: Given: limx→0-1+1x

Q: Find the limits in Exercise

A: We have to find the following limits -  limθ→0-(1 + csc θ)

Q: Calculate 5* – 4* lim

A:

Q: Evaluate 1- lim sırx

A:

Q: 3. Evaluate each limit: x'+7x+12 4x а) im b) lim x +2 x+3

A:

Q: Evaluate the limit lim X->00 8xナ9x 9x3-7

A:

Q: Evaluate the limit V9 + 5x? lim x → ∞ 7+ 2x

A:

Q: Inx 6. lim,

A:

Q: Evaluate the following limits

A: Given Equation:- limx→∞ 3+2x+4x2x2

Q: Evaluate lim (e* – 2.x) x→0-

A: To evaluate: limx→0-(e3x-2x)3x