Suppose that lim an = 5 and lim bn = 9. n-0 n→∞ Determine the limits. lim (an + bn) = n→∞o lim a = n48 lim cos (лbn) = n→∞ lim (a - 2an bn) = n→∞

Determine the following limits:

Find the limit of the following: -1 a. fim 4x-x-3 5x -3x b. lim- * 7x +1 6x + 5 c. lim 3x-8 d. lim sinr 2x-7 c. lim * cos x sin 5x f. lim g. lim 10(sin x-x) h. lim tan x

2. Evaluate, lim (3x+ y). (х,у)-(4,5)

Prove that lim √16x*+9y¹2 4x² +3y does not exist by showing that the limits along different (x,y) → (0,0) curves are distinct or not equal.

Use this graph of y = f(x): -5 -4 -3 -2 -1 _0←* lim f(x) = +0<* lim f(x) = →0 3 N to evaluate each of the following: lim f(x) = = 18 -1 -2Q 1 ƒ(0) Type DNE if the limit does not exist. 2 3 4 5 --។

Thank you for your assistance

Which of the following limits can be evaluated using L'Hôpital's Rule? 3х-12 A.lim X→4 x2 +16 3х -12 B. lim x→4 x2 – 16 12х-3 C.lim X→4 X -4 X - 4 D. lim x→4 12x -3

Evaluate the following limits and show your complete solution.

The direction along which lim ху —у =1 is (x,v) → (1,0) x² -6y²– 2x+1 1 +X- 3. %3D y3 -. None of these. y3 - 1. 1 y%3Dx+ 3. 1/3