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x2 +7x+12 1. Consider the function: f(x)= x +3 a. Is this function continuous at x...
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
1. Consider the function -F5 sin(r) for r f(x) =2 for 1< 3 2-25 for 3 x2 -9x + 20 Evaluate the following limits You do not have to cite limit laws, but you must show how you arrived at your answer If a limit Does Not Exist, explain why. You should use oo or -oo where applicable Calculating the limit using L'Hopital's Rule will receive NO CREDIT. (a) lim f(x) r-+0 (b) lim f(x)= z-1 (e) lim f(z) (d)...
3. (12) If the function below is continuous and differentiable everywhere within the interval [-3, 3), sketch the graph which satisfies the following conditions: f(-3) = 0, f(-2) = 3, f(-1) = 2, f(1) = -1, f(3) = -2 f'(-2)=0 f'(x) >0 on (-3,-2), f'(x) <0 on (-2, 3) f"(x) > 0 on (-1, 1), f '(x) <0 on (-3,-1) U(1, 3)
3. (12) If the function below is continuous and differentiable everywhere within the interval (-3, 3), sketch the graph which satisfies the following conditions: f(-3) = 0, f(-2) = 3, f(-1) = 2, f(1) = -1, S (3) = -2 f'(-2) = 0 f'(x) > 0 on (-3,-2), f '(x) <0 on (-2, 3) f"(x) > 0 on (-1, 1), f '(x) <0 on (-3,-1) (1, 3)
the function y=f(x)={ 0-4), 14x+16, x20 x<0 Consider 1. (a) Sketch the graph off. (3 pts.) (b) Verify that the function is continuous everywhere using the properties of the definition and possibly calculating the limit at a particular point. (2 pts.) (c) Show f'(x) is not continuous at x-0. (5 pts.) the function y=f(x)={ 0-4), 14x+16, x20 x
Consider the function f(x) = Σ (a) Where is f defined? (b) Where is f continuous? (c) Where is f differentiable? Consider the function f(x) = Σ (a) Where is f defined? (b) Where is f continuous? (c) Where is f differentiable?
7. Consider the function f:R + R defined by f(x) = x < 0, 3 > 0. e-1/x2, Prove that f is differentiable of all orders and that f(n)(0) = 0 for all n e N. Conclude that f does not have a convergent power series expansion En Anx" for x near the origin. [We will see later in this class that this is impossible for holomorphic functions, namely being (complex) differentiable implies that there is always a convergent power...
2x-8 The rational function f(x)= - x2-7x+12 - has ... A horizontal asymptote at y = 2 ro A horizontal asymptote at y = 0 A horizontal asymptote at x = 2 d. A horizontal asymptote at x = 3 The domain of f(x)=log3(x) is... xin(-xxx) xin (0,x) , xin [0,x) x in(-3,0) 2x -8 The rational function f(x)=- x? -7x+10 has... - a hole at x = 3 and a VA at x =4 ന hole at x =...
7) [f function g is defined by g(x) = Ta'an, xa, thon g'(1) = ? (A) 1 (B) 2 (C) 3 (D)O (E) Does not exist The graph of function g is shown below. Which of the following statements about function g is true? A) Atx=b, function g is differentiable. BY Atxa, function g is continuous, but not differentiable. C) Atx=a, function g is both continuous and differentiable Function g is not differentiable at any point. E) Atx=c, function g...
#7 and #8 UVOD f(x) 7x X2 + 8 1 SXS 3 lim n- 1 Need Help? Radt Wish Talk to a Tutor 8. [-/1 Points) DETAILS Use the Definition to find an expression for the area under the graph off as a limit. Do not evaluate the limit. Fx) x2 + 12x 3 SX 85 lim