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True and False Questions for Calculus
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Terms in this set (30)
The product of two odd functions is odd
False
The product of two even functions is odd
False
If cos(x) = y has a solution in [0,2pi), then cos(x) = -y has a solution in [0,2pi).
True
Odd functions are symmetric about the x-axis
False
Even functions are invertible over their entire domain
False
cos^-1(cos(x)) = x for 0 < x < 2pi
False
sin(sin^-1(x)) = x for -1 < x < 1
True
If cos^-1(x) = y for x in [0,1], then cos^-1(-x) = -y.
False
If lim x->a f(x) = L, then f(a) = L
False
Let R(x) = p(x)/q(x) be a rational function. If the degree of p(x) is greater than the degree of q(x), then R(x) has at horizontal asymptote at y=0
False
A function can have at most 1 horizontal asymptote
False
The range of cos^-1(x) is (-pi/2, pi,2)
False
The limit of sinx/x as x->infinity is 1
False
Lim x->-infinity (x^6^1/3) = x^3
False
If f^-1 is continuous on its domain, then f is continuous on its domain
True
If f is continuous from the right and from the left at a then f is continuous at a
True
Suppose you are given that x lies in the interval (2,8) and x cannot = 4, then the smallest delta such that 0 < |x-4| < delta is 2
False
The function x^1/3 is differentiable at every point on its domain
False
Let f(x) = e^kx for k<0. Then f^(n) (x) = k^n e^kx
True
Assume f(x) and g(x) are differentiable at x, and let p(x) = f(x)g(x). Then p'(x) = f'(x)g'(x)
False
Knowing that f(x) and g(x) are differentiable at x is enough to imply that the derivative of q(x) = f(x)/g(x)
False
The instaneous rate of change in area of a circle with respect to the radius r is equal to the perimeter of the circle
True
The speedometer on a car measures average velocity
False
An object can have positive acceleration and decreasing speed
True
The function xcos(x) can be differentiated without using the chain rule
True
A function of the form f(x) = e^h(x)ln(g(x)) is always defined
False
d/dx sin^-1(sin(x)) = 1
False
If a function is differentiable, then it is twice differentiable
False
Every invertible function is differentiable
False
The function tan(x) is invertible on the domain [-pi/x, pi/2]
False
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