Calc chp2

If f '(r) exists, then lim x→r f(x) = f(r).

true

If f is continuous at 5 and f(5) = 3 and f(4) = 3, then lim x→2 f(4x2 − 11) = 3.

true

If f is continuous on [−1, 1] and f(−1) = 4 and f(1) = 3, then there exists a number r such that |r| < 1 and f(r) = π.

true

If p is a polynomial, then lim x→b p(x) = p(b).

true

The average rate of change between two points is the slope of the line containing those points.

true

The derivative of a function at a point is the slope of the tangent line at that point.

true

The equation x10 − 10x2 + 7 = 0 has a root in the interval (0, 2).

true

The slope of the tangent line at the point x = a of the function f(x) is m = lim h→0 f(a + h) − f(a) h .

true

ssume f is a continuous function. If f(a) > 0 and f(b) < 0 then by the Intermediate Value Theorem there is a point c is in (a, b) such that f(c) = 0.

true

If f(1) > 0 and f(8) < 0, then there exists a number c between 1 and 8 such that f(c) = 0.

false

If f(x) > 7 for all x and lim x→0 f(x) exists, then lim x→0 f(x) > 7.

false

If f(x) is a rational function, then there is always a point x = a such that lim x→a f(x) = ∞.

false

If f(x) is not defined at c, then f(x) cannot be continuous on any interval.

false

If lim x→0 f(x) = ∞ and lim x→0 g(x) = ∞, then lim x→0 [f(x) − g(x)] = 0.

false

If the function f is increasing on an interval, the derivative of the function should be negative on that interval.

false

d2y dx2 = dy dx 2

false

A continuous function is always differentiable.

false

A function is called continuous at a point if the limit exists at that point.

false

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

false

If lim x→9 f(x) = 0 and lim x→9 g(x) = 0, then lim x→9 f(x)/g(x) does not exist.

False

If lim x→5 f(x) = 5 and lim x→5 g(x) = 0 , then lim x→5 f(x) /g(x) does not exist.

True