Calculus Exam 1 True/False mine

If f is a function, then f(s+t) = f(s) + f(t)

False

d/dx (10^x) = xln(10)

False

if f is a one-to-one then f^-1(x) = 1 /f(x)

False

If f(x)=2, then f'(x) = 1

False

If a function is continuous, then it is differentiable

False

If f "(2) = 0, then (2, f(2)) is an inflection point on the graph y = f(x).

False

If f has domain [0, infinity) and the graph of f has no horizontal asymptote then, lim f(x) = infinity or lim f(x) = -infinity

False

If f is continuous on [a,b] then f attains an absolute maximum value f(c) and an absolute value f(d) at some numbers c and d in (a,b).

False

If lim f(x)= 0 as x->7, and lim g(x) =0 as x-> 7, then lim x-> 7 [f(x)/g(x)] does not exist.

False

If the slope of the tangent line is 2, the slope of the normal line is 1/2.

False

If x>0 and a>1, then lnx/lna = ln(x/a)

False

If y= e^x, then y' = 2e

False

d/dx (f(g(x))) = f'(x)g(x) + f(x)g'(x)

False

f'(c) = ((f(c+h) - f(c))/h).

False

if x is any real number, then sqrt x^2 = x

False

lim x--> infinity x/e^x = 1

False

tan^-1 x = sin^-1 x/cos^-1 x

False

If f is continuous on [-7,7], and f(-7) =4 and f(7) = 3, then there exists a number r such that |r| < 7 and f(r) = pi

True

If lim x->a f(x) exists but lim g(x) x--> a does not exist, then lim x-> a [f(x) + g(x)] does not exist.

True

If p is a polynomial then lim p(x) x-> b = p(b)

True

If the derivative of f(x) exists at x=a, then lim x-> a f(x) = f(a)

True

If y=f(x), then its derivative f'(x) = lim x->a (f(x)-f(a))/(x-a).

True

The function f(x) = x^2 and g(x) = x^2 +2 have the same derivative

True

The slope of the graph of y=x^2 is different at every point on the curve

True

an equation of the tangent line to the parabola y=x^2 at (-2,4) is y=-4x-4

True

d/dx (y^2) = 2y dy/dx

True

if f'(x) exists and is nonzero for all x, then f(1) cannot = f(0)

True

if the tangent line to the graph of f is horizontal at the point (a,f(a)), then f'(a) = 0

True

the slope of the graph of y=f(x) at the point (1,f(1)) is m = f'(1)

True

there exists a function f such that f(x)>0, f'(x)<0, f''(x) >0 for all x

True