Calculus

EXPERT ANSWER

EXPERT ANSWER a) When x = 0, we are talkin about the y-axis And when they ask us to find the limit as x —> 0(-), we are looking at the value of y when x is approaching 0 from the negative side. Notice that at x = 0, y = 3. Also, when x …

In these exercises, make reasonable assumptions about the graph of the indicated function outside of the region depicted. For the function g graphed in the accompanying figure, find lim x right 0- g(x) lim x rightarrow 0+ g(x) lim x rightarrow 0 g(x) g(0). Read More »

Sketch the graph of the function. f(x) = 4 + x if x < −2 x2 if −2 ≤ x < 2 6 − x if x ≥ 2 Use the graph to determine the values of a for which lim x → a f(x) does not exist. (Enter your answers as a comma-separated list.) a = EXPERT ANSWER

Sketch the graph of the function. f(x) = 4 + x if x < ?1 x2 if ?1 ? x < 1 2 ? x if x ? 1 Use the graph to determine the values of a for which lim x ? a f(x) does not exist. (Enter your answers as a comma-separated list.) a = EXPERT ANSWER

2.)Use the given graph of f to state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.) (a) lim x → 2− f(x) (b) lim x → 2+ f(x) (c) lim x → 2 f(x) (d) f(2) (e) lim x → 4 f(x) (f) f(4) EXPERT ANSWER

For the function f whose graph is given, state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.) (a) lim x?1 f(x) (b) lim x?3? f(x) (c) lim x?3+ f(x) (d) lim x?3 f(x) (e) f(3) EXPERT ANSWER

Sketch the graph of the function. f(x) = 3 + x if x < −2 x2 if −2 ≤ x < 2 6 − x if x ≥ 2 *The lower left hand graph is the correct graph!Use the graph to determine the values of a for which lim x → a f(x) does not exist. (Enter your answers as a comma-separated list.) a = EXPERT ANSWER

Sketch the graph of an example of a function f that satisfies all of the given conditions. lim x → 0− f(x) = 2, lim x → 0+ f(x) = −1, f(0) = 1 EXPERT ANSWER

For the function h whose graph is given, state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.) EXPERT ANSWER (a)     lim x → −3− h(x)= (b)     lim x → −3+ h(x)= (c)     lim x → −3 h(x)= (d)     h(−3)= (e)     lim x → 0− h(x)= (f)     lim x → 0+ h(x)= (g)     lim x → 0 h(x)= (h)     h(0)= (i)     lim x → 2 h(x)= (j)     h(2)= (k)     lim x → 5+ h(x)= (l)     lim x → 5− h(x)= EXPERT ANSWER a) 4b)4c)4d)DNEe)1f)-1g)DNEh)1i)2j)DNEk)3 l)from the …

For the function h whose graph is given, state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.) Read More »

For the function R whose graph is shown, state the following. (If an answer does not exist, enter DNE.) (a) lim x ? 2 R(x) (b) lim x ? 5 R(x) (c) lim x ? ?3? R(x) (d) lim x ? ?3+ R(x) (e) The equations of the vertical asymptotes. x = (smallest value) x = x = (largest value) EXPERT ANSWER a) At x = 2, both sides …

For the function R whose graph is shown, state the following. (If an answer does not exist, enter DNE.) Read More »