Please solve each question and show work please, also can you write clearly so I can understand, thanks a million

91121.1 Please sign (or type) your name below the following honor pledge: i have completed this quiz by myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this quiz. Name Date 1. (S 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) 2. (10 POINTS) Evaluate the limit as x approaches 4 of the following rational expression: . x3+x216x16 lm' : er x23x4 Use table of values to find the limit; write only the values, not the arithmetic operations: ----- 3. (5 POINTS) For what values ofx the following function is discontinuous? ( explain your answer, you can use the graph ofthe function) 2 x + 3x + 5 f (X) = '2 x + 3x 4 4. (10 POINTS) Evaluate the limits using algebraic properties of the limits. . Vx-lZ a. 11m = xi5 xS 7-H. _ b. lim 2" x 1 = xrl xl 5. (10 POINTS) Evaluate the limits using algebraic properties of the limits. . 1COSI a. 11m . 2 = x90 sm x . sin(3x) b. hm = x->0 5x 6. (20 POINTS) Evaluate the limits. Use Squeezing Theorem . 2 . 1 0. [mm x 5m - x>D x . 1 b. ltmx2 cos . x>O x 7. (15 POINTS) Use the Intermediate Value Theorem to verify that given function has a root in the given intervalis). Then use the Bisectlon Algorithm to narrow the location of that root to an interval of y = x3 ~ 32:2 + 3 on [ 1, 0]. After calculating, represent your answer graphically. 8. (15 Points) Given the limit airing (2x 5) = 1, find 6 such that l(2x - 5) 1|