Please solve each question and show work in conjunction with nice handwriting, please and thanks a million!

1. 3. 4. S. 6. 7. 8. (5 POINTS EXTRA CREDIT) What is the equation of the line tangent to the parabola y = x2 + x 2 at the point (2, 4). Use limit definition to calculate the slope of the tangent line at the point (2, 4} (10 POINTS) Evaluate the limit as x approaches 4 of the following rational expression: 1' x3+x216x16_ x' x23x4 ' Use table of values to find the limit; write onl the values, not the arithmetic oerations: _______I- ________ (5 POINTS) For what values of x the following function is discontinuous? {explain your answer, you can use the graph of the function} 2 x + 3x + S {(x) = 2 x + 3x 4 (10 POINTS} Evaluate the limits using algebraic properties of the limits. . Jx12 a. llm = x-v5 Jig5 b. lim 2" "x" = xd] X-I (10 POINTS} Evaluate the limits using algebraic properties of the limits. . lCOSX a. [HT] .2 = 100 sm x . sin 3x b. 11111 C }= 1300 5X (20 POINTS) Evaluate the limits. Use Squeezing Theorem . . 1 a. hm 1t:2 3m 1-00 X . 2 1 b. itmx cos- . x0 x (15 POINTS} Use the Intermediate Value Theorem to verify that given function has a root in the given intervalls). Then use the Bisection Algorithm to narrow the location of that root to an interval of y = x3 3x2 + 3 on [- 1, 0}. After calculating, represent your answer graphically. [15 Points) Given the limit lim (2x 5) = 1, find (5' such that |(2x 5) 1|