In Exercises 13-22, find the limit of each rational function (a) as x→0o and (b) as x→ -00. 2r + 7 x3 - x? + x + 7 2x + 3 13. f(x) 14. f(x) 5x + 7 16. fX) =2 Зх + 7 x² – 2 15. f(x) x + 3 9x + x 7x3 x3 - 3x2 + 6r 17. h(x) 18. h(x) %3D 2x4 + 5x2 — х + 6 x³ + 7x? – 2 x² – x + 1 10x + x4 + 31 19. g(x) 20. g(x) 3x7 + 5x² – 1 6x3 – 7x + 3 5x8 – 2r3 + 9 21. flx) : 22. h(x) 3 +x – 4x

Q: lim as x approaches 4 from the right of 8-2x/|x2-x-12| a. 2  b.-2  c. -1  d. 4  e. infinity

A: The given expression is,

Q: Define f(x) = 2 – 3x? What is the domain of this function? (-00, 2) (-00, 2] [-3, 0) (-x0, 0) [0, 0)

A:

Q: lim Explain each Step.

A:

Q: lim (√x³ – 5x² – x) _ x →∞

A:

Q: .iF A={A,B,C} WHICH OF THESE REALTIONS ARE A FUNCTION?Explain ? a){(a,b),(b,c),(c,c)}…

A: Step:-1 Function:- A relation is a function if each input (that is, each element in domain) has only…

Q: Refer to the functions f and g and evaluate the functions at x =-2. f = {(2, -1), (1, 1), (-4, -6),…

A: (f+g)(-2)=f(-2)+g(-2)  Substitute   f(-2)=-8  ,    g(-2)=-5in the above equation

Q: Select the equation of the parabola with vertex (3, 2) and directrix y=-1. O(x-3)² =12(y-2) ○ (x-3)²…

A:

Q: 3 2 -1 -4 +2 -1 1 4 6. -1- -2 -3 -4

A:

Q: 6. Use the e, 8 definition to show that lim,2 x + 1 x+ 3 emlin

A:

Q: 15) In Exercises 91–94, use the graphs of f and g to evaluate each composite function. 4 3+ 2 y =…

A: (fog)(x) = f[g(x)]

Q: lim I+00 82-71 ||

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.