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Please show work on how to solve? (49. Show that the function (x2 +3 for x...
2 *3 X3 6. Consider a function y = f(x) such that lim f(x) = 2, lim f(x) = 2, and f(3) = -1. Explain whether each statement is true or false. a) y=f(x) is continuous at x = 3. b) The limit of f(x) as x approaches 3 does not exist. c) The value of the left-hand limit is 2. d) The value of the right-hand limit is -1. e) When x = 3, the y-value of the function...
real analysis 1,3,8,11,12 please 4.4.3 4.4.11a Limits and Continuity 4 Chapter Remark: In the statement of Theorem 4.4.12 we assumed that f was tone and continuous on the interval I. The fact that f is either stric tric. strictly decreasing on / implies that f is one-to-one on t one-to-one and continuous on an interval 1, then as a consequence of the value theorem the function f is strictly monotone on I (Exercise 15). This false if either f is...
Evaluate the piecewise defined function at the indicated values (x2 f(x) if x -1 6x if 1 < x s 1 = -1 if x > 1 f(-3) (- 3 2 f(-1) f(0) = f(30) =
Sketch a graph of a function f(x) that satisfies each of these conditions. f (x) has a jump discontinuity at x = -3, and a displaced point at x = -1 f (x) is continuous on lim f( -oo) lim f(x 2) lim f(r oo) -0+ F-1) f(0)=0 (-oo, -3), -3, 1), (-1,0, (0, o lim f( -oo) lim f(x 2) lim f(r oo) -0+ F-1) f(0)=0 (-oo, -3), -3, 1), (-1,0, (0, o
send help for these 4 questions, please show steps Definition: The AREA A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles A = lim R, = lim [f(x)Ax +f(x2)Ax+...+f(x)Ax] - 00 Consider the function f(x) = x, 13x < 16. Using the above definition, determine which of the following expressions represents the area under the graph off as a limit. A. lim...
(1 point) A function f is said to have a removable discontinuity at a if: 1. f is either not defined or not continuous at a. 2. f(a) could either be defined or redefined so that the new function is continuous at a. Let f(x) = 2x2+6x–80 X-5 Show that f has a removable discontinuity at 5 and determine the value for f(5) that would make f continuous at 5. Need to redefine f(5) =
Find the domain of the following function. X +3 f(x)= x2 - 49
1-Given the function: \(y=\frac{x^{2}-3 x-4}{x^{2}-5 x+4}\), decide if \(f(x)=y\) is continuous or has a removable discontinuity, and find horizontal tond vertical asymptotes.2 A-Use the definition \(\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}\) to prove that derivative of \(f(x)=\sqrt{4-x}\) is \(\frac{-1}{2 \sqrt{4-x}}\)2 B- Evaluate the limit \(\lim _{h \rightarrow 0} \frac{f(x+h) - f(x)}{h}\) for the given value of \(x\) and function \(f(x) .\)$$ f(x)=\sin x, \quad x=\frac{\pi}{4} $$3-Given the function: \(y=(x+4)^{3}(x-2)^{2}\), find y' and classify critical numbers very carefully using first derivative tess...
Question 86 - 100: Look at the graph of function f(r) . A -5 -1 3 5 7 9 11 1--1 86. lim f(x) = 87. lim f() = 88. Is f(x) continuous at I = 1? 89. Is f(x) continuous at x = 0? 90. Is f(x) continuous at x = - 3 from the left hand side ? 91. limf() = 92. Does limf (x) exist ? 93. Is f(x) continuous at I = 8? 94. Is f()...
Question 1 (1 point) Use the figure shown to answer the following question aboutf(x). What is the limfm)? (-2,2), 2 (0.1) (3.0) I -4 -3 -2 - 1 2 4 5 (-2-1) (3-1) -1 -2 1) The limit does not exist. 2) The limit is 1 3) The limit is 3 4) The limit is 0. Question 2 (1 point) Question 2 (1 point) Use the figure shown to answer the following question. What is the lim f(x)? (6,5), (1.4)...