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