For each of the following functions f(x) below : Find its limits limx→±[infinity]f(x) as x approachs ±[infinity] . Choose the values of x where f(x) is differentiable, i. e. f′(x) exists Choose the values of x where f(x) is also strictly increasing, i. e. f′(x)>0 . For f(x)=max(0,x) : (If the limit diverges to infty, enter inf for [infinity], and -inf for −[infinity] ) limx→−[infinity]f(x)=

See below

Step-by-step explanation:

then f(x)=0 if x<0 and f(x)=x if x≥0.

When x→-∞, f is the constant function zero, therefore . When x→∞, f(x)=x and x grows indefinitely. Thus

f is differentiable if x≠0. If x>0, f'(x)=1 (the derivative of f(x)=x) and if x<0, f'(0)=0 (the derivative of the constant zero). In x=0, the right-hand derivative is 1, but the left-hand derivative is 0, hence f'(0) does not exist,

f'(x)>0 for all x>0. Therefore f(x) is strictly increasing on the inverval (0,∞).

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,