Select the second function, y = 1x2, for 0 < x ≤ 5.(a) Observe the graph of A(t) = t1f(x) dx in the second diagram. Does it appear that lim x → ∞ A(t) exists?YesNo    (b) Change the maximum value of x to 100 and observe the graph of A(t) again. Does it appear that lim x → ∞  A(t) exists?YesNo    If so, estimate the value of the limit. (If an answer does not exist, enter DNE.)lim x → ∞  A(t) = (c) Find the values of A(1000), A(10,000), and A(100,000).A(1000)  =  A(10,000)  =  A(100,000)  =  (d) The graphs of the first two functions (from the pull-down menu) look very similar. Can you explain why lim x → ∞  A(t) exists for one of the functions but not the other?

Use the graph of f to estimate each limit, or write und (meaning undefined) if no limit exists. Use inf for ∞.limx→1−f(x)= limx→1+f(x)= limx→1f(x)=

Can you explain why lim x → ∞  A(t) exists for one of the functions but not the other?

Describe the behaviour of the graph of the function as x → – ∞ and as x → ∞.

For the function A whose graph is shown, state the following. (If the limit is infinite, enter '∞' or '-∞', as appropriate. If the limit does not otherwise exist, enter DNE.)The x y-coordinate plane is given. The function enters the window in the second quadrant, goes up and right becoming more steep, exits just to the left of x = −3 in the second quadrant nearly vertical, reenters just to the right of x = −3 in the second quadrant nearly vertical, goes down and right becoming less steep, crosses the x-axis at x = −2, goes down and right becoming more steep, exits the window just to the left of x = −1 in the third quadrant nearly vertical, reenters just to the right of x = −1 in the third quadrant nearly vertical, goes up and right becoming less steep, crosses the y-axis at approximately y = −0.6, changes direction at the approximate point (0.5, −0.5) goes down and right becoming more steep, exits the window just to the left of x = 2 in the fourth quadrant nearly vertical, reenters just to the right of x = 2 in the first quadrant nearly vertical, goes down and right becoming less steep, crosses the x-axis at x = 3, changes direction at the approximate point (4.5, −1.5), goes up and right becoming more steep, crosses the x-axis at approximately x = 6.5, and exits the window in the first quadrant.(a)lim x → −3 A(x) (b)lim x → 2− A(x) (c)lim x → 2+ A(x) (d)lim x → −1 A(x) (e)The equations of the vertical asymptotes. (Enter your answers as a comma-separated list.)

For the function f whose graph is shown, state the following. (If the limit is infinite, enter '∞' or '-∞', as appropriate. If the limit does not otherwise exist, enter DNE.)FigureThe x y coordinate plane is given. Refer to the adjacent description for more details.Description(a)lim x → −7 f(x)(0,2) (b)lim x → −3 f(x)DNE (c)lim x → 0 f(x)2 (d)lim x → 6− f(x)∞ (e)lim x → 6+ f(x)−∞ (f)the equations of the vertical asymptotes (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)x = (−3,6)