By using the e –- N definition of limits, prove пз — Зп - = 1. lim п00 п3 — п — 2

Sfsin(r – y kýyd . B. (i) Evaluate 00 sVx+1 lim (ii) Evaluate * 4Vx +3

Find the limits of the following indeterminate forms:

Evaluate the limit of the ff:

Evaluate the limit

Evaluate the following limits. If needed, enter oo for oo and -oo for – 00. (a) lim (382? – 38r*) = I+ 00 (Б) lim I - 00 (382? – 382) 38z")

Evaluate the limit and show if it produces an indeterminate form

The limit, lim h→0 2(x + h)² - 2x² h lim h→0 2(x +h)² - 2x² h To find this limit, the FOIL method can be used to expand the expression in the numerator. Then, simplify the numerator; distribute to remove the parentheses and combine like terms. = = = lim h→0 lim h→0 7 lim h→0 has the indeterminate form 2(x2 + 2x² + 4xh + h h 0 at h = 0 and h is a common factor of the numerator and denominator. 0 h h²) - : 2x² xh xh + 2h² - 2x² We cannot let h→0 until the factor h is removed from the denominator. Notice that the two remaining terms in the numerator of the result have a common factor of h.

Evaluate the following limits

4. Show the IVT root on the function fix) = 2X²³-2x²-3x+1 on [1, 2] 5. Find i limx-100 √x²+2-X -4x²-3x+10 6. Evaluate the limit, limx-s= 2X² +8x²-3x+1