True-False

If p is a polynomial, then limit as x→b of p(x) = p(b).

True

Let f be a continuous function on the interval [a,b]. Then there exists a number c in [a,b] such that f(c) = f avg .

True

Polynomial functions are differentiable on (-∞,∞).

True

The equation x^4-6x^2+5 = 0 has a root in the interval (0,2).

True

The function f(x)=sin(x), − π/2≤x≤π/2 , is one-to-one.

True

The inverse function of y=e^(3x) is y=1/3lnx.

True

ln(1/10)=-the intergral between 1 and 10 of 1/xdx.

True

Let f be a function satisfying f(a) = k, then the limit as x→a of f(x) = k.

False

Rational functions are differentiable on (-∞,∞).

False

Suppose f' exists. The domain of f' coincides with the domain of f.

False

The average value of the function f(t)=sec^2(t) on the interval [0,π/4] is f avg = 1.

False

The integral between 0 and π/2 of cos^2(x)dx = -the integral between 0 and 1 of u^2du.

False

d/dx(10^x)=x10^(x-1).

False

the limit as x→4 of (2x/x-4)-(8/x-4) = limit as x→4 of 2x/x-4 - limit as x→4 of 8/x-4.

False

Every continuous function has a continuous antiderivative.

True

If f' is continuous and f'(x) =/ 0 for all x, then f(0) =/ f(x)

True

Consider the region R bounded between the curves y = x and y = x^3 . The area of R is 0.

False

Every continuous function has a continuous derivative.

False

If f and g are increasing on (a,b), then f*g is increasing on (a,b).

False

If f is continuous at x = a, then f is differentiable at x = a.

False

If f is continuous on [a,b], then d/dx(the integral between a and b of f(x)dx)=f(x).

False

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

False

If f'(c)=0, then f has a local maximum or minimum at c.

False

If x>0, then (ln x)^6=6lnx.

False

If |f| is continuous at a, so is f.

False

If f(-x)=-f(x) for all x in the interval [-a,a], a>0, then the integral between -a and a of f(x)dx=0.

True

If f and g are continuous on [a,b], then the integral between a and b of f(x)+g(x) dx = the integral between a and b of f(x)dx + the integral from a to b of g(x)dx.

True

If f has a local maximum or minimum at c, then f'(c)=0.

True

If f is a continuous function on [a,a+h], then lim h→0+ f avg = f(a).

True

If f is differentiable at x = a, then f is continuous at x = a.

True