A)lxl=x if x_<0 B)l x-a l is the distance from x to a C)If X,Y AND Z are any rea

ID: 3345677 • Letter: A

Question

A)lxl=x if x_<0

B)l x-a l is the distance from x to a

C)If X,Y AND Z are any real numbers, then it is always the case that l x-yl _<l x-z l + l z-y l.

D)The function cot (x) is the inverse of the function tan(x).

E)The function e^x is the inverse of the function ln(x).

F)The range of an invertible function is the domain of its inverse.

G)The function sin(x) is invertible on [-pi/2,pi/2].

H)Relative to the graph of y=sin(x), the graph of y=3sin(x) is stretched by a factor of 3 horizontally.

I)Relative to the graph of y=x^2, the graph of y=(x-2)^2 is shifted to the right by 2 units.

J)The graph of an even functon is symmetric through the y-axis.

K)If f(x) is continuous at a point a, then f(x) is differentiable at a.

L)Every continous function on the closed interval [a,b] attains a minimum value on the interval.

M)If a function attains a maximum value on the closed interval [a,b] attains a minimum value on the interval.

N)If a function attains a maximum value on the closed interval [a,b] at a point c, then f'(c)=0.

O)If lim (x->a+) f(x) and lim (x->a-) f(x) exist, then lim (x->a) f(x) exists.

P)If lim (x->a) f(x)exists, then f(a) must be defined.

Q)lim(theta->0) sin (theta)/theta=1

R)If f''(2)=0, then (2,f(2)) is an inflection point on the curve y=f(x).

S)A function can have at most one antiderivative.

T)If f(x) is continuos on the closed interval [a,b], then the definite integral integral (b,a) f(x) dx must exist.

U) If f(t) is continous and F(t) is any antiderivative of f(t), then it is always the case that integral (b,a) f(t) dt= F(b)-F(a).

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