Prove that lim ((2x+3)/(x^2 +5))=1/2 as x approaches 2.
Use the definition to prove lim x +4 - X -1 2x + 1
3 Use the 2-3 definition of lim f(x)=1 to prove that lim x+8 = 14.
Evaluate the limit lim x→5 x^2 −2x−15/ x^2 −25 Evaluate the limit lim x→∞ x^2 + x /x^5 c. Find all points on the graph of f(x) = 2x^3 −x where the tangent line is parallel to the line y = 149x + 7.
limit practice problems 1) lim x² - 2x+1 X 1 x² + 3x+2 2) lim x-1 X 3+ x² - 6 x² 6 3) lim x-1 X +3 X-3
2. Prove that lim (-1)"+1 0. 72-00 n 2n 3. Prove that lim noon + 1 2. 80 4. Prove that lim n-+v5n 0. -7 9 - in 5. Prove that lim n0 8 + 13n 13
2. Week 1 Competency: Partial fraction 2x +3 (2x +5)(x-3) Prove that your partial fraction result is correct by adding it up.
m2 2. Prove that lim -+0n3 + 1 -=0. 3 5 100 3n2 + 2n - 1 3. Prove that lim = 5n2 +8 cos(n) 4. Prove that lim = 0. n-700 m2 + 17 5. Prove that lim (Vn+1 - Vn) = 0 Hint: Multiply Vn+1-vñ by 1 in a useful way. In particular, multiply Vn+1-17 by Vn+1+vn
3. Evaluate the limits x-2 (a) lim 2 (c) lim x-,2x2 +2 ?- (b) lim 2 im 2x +4 (d) Given f(x)x1 -1<x s 2 3-?
just number 16 15-42 Find the limit or show that it does not exist. 1 x2 3x 15. lim 2 16. lim 3 x00 x x +1 2x+ 1 ズ→00 4x3 6x2- 2 x-2 17. lim 18. lim x21 2x3 4x 15-42 Find the limit or show that it does not exist. 1 x2 3x 15. lim 2 16. lim 3 x00 x x +1 2x+ 1 ズ→00 4x3 6x2- 2 x-2 17. lim 18. lim x21 2x3 4x
cewise Functions e function, evaluate lim f(x). 2 1-2x²+x+3 f(x) = { 2x2 – 3x + 3 (-3x - 2 if if xs1 1<x< 6 if x26 below: