6. Where are the following functions discontinuous? a) f(x) = x+2) x+2 (x+2)x b) f(x) =...
1 6. Where is the function f(x) { { - X4 if x # 0 discontinuous? if x = 0 0 Is this a removable discontinuity? ex if x < 0 7. Where is the function f(x) discontinuous? x2 if x > 0 Is this a removable discontinuity? Is it a jump discontinuity? f(x) = {
a) Show that f is discontinuous at any x 6=
0.
b) Show that f is continuous at x = 0.
c) Show that f is differentiable at x = 0 and compute
the value f 0 (0).
d) Show that f is not integrable on the interval [1, 2]
(or any interval, but I don’t mind if you use that interval
specifically).
(x2 (x EQ) f(x)=o (x &Q)
Find all values x= a where the function is discontinuous. 7 if x <4 f(x) = x- 9 if 4 sxs7 7 if x>7 O A. a=7 O B. a=9 OC. a=4 OD. Nowhere
suppose f(x)=x^2+x-6 for x does not equal 2 and f(x)=3 for x=2. Then which of the following statements are true? (I) f(x) is continuous on (-∞, ∞). (II) f(x) is discontinuous at 2 because f(2) is undefined. (III) f(x) is discontinuous at 2 because lim x→2 f(x) does not exist. (IV) f(x) is discontinuous at 2 because lim x→2 f(x) ≠ f(2).
Find all values x = a where the function is discontinuous. 3x - 5 if x < 0 f(x) = x2 + 5x -5 if x 20 O A. a = 0 OB. Nowhere O c. a = 5 OD. a = -5
Find the value x a where the function is discontinuous For the point of discontinuity give (a) f(a) if it exists. (b) limfx). (c) lim f(x), (d) lim 1x), and (e) identify which conditions for continuity Affx) are not met 10 a= (Use a comma to separate answers as needed) (a) Select the choice below and, if necessary, fill in the answer box within your choice O A 8a)= OB. f(a) is undefined (b) Select the choice below and, if...
(a) Graph the given function, (b) find all values of x where the function is discontinuous, and (c) find the limit from the loft and the right at any values of x where the function is discontinuous 4x2 x) X-3x+ 2 x>0 xs0 (a) Choose the correct graph below O dos (b) Select the correct choice below and, if necessary, fill in the answer box within your choice, O A. The function is discontinuous at (Use a comma lo separate...
For f(x) = 2-x and g(x) = 2x2 +x+6, find the following functions. a. (fog)x); b. (gof)(x); c. (fog)(2); d. (gof)(2) a. (fog)(x) = 0 (Simplify your answer.) b. (gof)(x) = 0 (Simplify your answer.) c. (fog)(2)- d. (gof)(2)-
please help
#2(b)) What types of functions are f(x) = e" and g(x) = x". Compare the differentiation formulas for f and 9 # 3,4,6,11,14,19.21) Differentiate the function: # 3) f(x) = 186.5 # 4) f(1) = 30 # 6) (t) = {- 36 +t #11) G(x) = VI - 2* # 14) R(r) = YTO #19) y = +*+47 +3 # 21) v = # 25) Find the equation of the tangent line and normal line to the curve...
3) Sketch the graph of the following rational functions. 2 a. f(x) = + +5r+6 x + 1 b. f(x) - 4x - 32 4) Solve each inequality. Give each solution in interval notation. a. + +8r+15 so b. 2x-5x > 3 C. (x - 1)(x+3)(x+5) > 0 x+3 d. > 0 x² - 5x+6 X +3 <2 2x+4 e.