11. The limit of f as x approaches a may not exist. Which of the folowing statement(s) is/are true? i. If f(x) becomes infinitely large in magnitude (positive or negative) as x approaches the number a from either side, then lim f(x) = c0 or lim f(x) = -0o. In a either case, the limit does not exist. ii. If f(x) becomes infinitely large in magnitude (positive) as x approaches a from one side and infinitely large in magnitude (negative) as x approaches a from the other side, then limf(x) does not exist. If lim f(x) = L and lim f(x) = M, and L + M, then limf(x) does not exist. a ii. a O A. iii only B. i and i only C. i and ii only O D. i, ii, and i

Q: B. The graph of f(x) is given in Figure 5. Determine the following limits: 1. lim f(x) x→-4 4. lim f…

A: We know that for any given functiony=fx at x=a limit will exist, if limx→a-fx=limx→a+fx…

Q: 8. Evaluate the limit by using a √√x-2 a. lim x8x8

A:

Q: x² + x – 6 - f. lim "3 x² – 9 /x + 1 – 2 g. lim х — 3 * 3 x - 8 h. lim * 2 2 x- 2 3x2 + 5x - 2 i.…

A: Given tha

Q: Let f(x) be the piecewise defined function a.-23.80 O b. 23.80 O c. -4.70 O d.-29.80 e. This limit…

A:

Q: 2. Sketch the graph of the function and use it to determine the following limits. (-x + 1 if x 1…

A: We can find the answer as below

Q: Given the peicewise-defined function f. x² + 14 if - 10 < a < - 2 - 2 < a < 5 f(x) = - 44 if - x² –…

A: Given the piecewise-defined function f(x) = x2+14if  -10≤x&lt;-2-44if  -2≤x≤5-x2-19if  5&lt;x&lt;11

Q: 10. Use the definition of limit to show that a. lim (x² + 4x) = 12, Z-2

A:

Q: 2. a) For what values of x is f discontinuous? b) At each point where f is discontinuous,…

A:

Q: For the function g(x) graphed here, find the following limits or explain why they do not exist. a.…

A: The graph of the function g(x) is shown as,Since parts a to c are already solved in original…

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.