1
APMA 1090 Final Questions with Answers (100% Correct
Answers)
indeterminate forms Answer: when f(x) isn't continuous at c, may
result in 0/0...etc, need to rewrite to solve
difference quotient Answer: f(x+h)-f(x)/h, used to find the slope of the
tangent line
heaviside function Answer: H(x) = {0 x < 0, 1 x >= 0}
squeeze theorem Answer: If f(x) <= g(x) <= h(x) for x near a, and limx-
>a f(x) = limx->a h(x) = L, then limx->a g(x) = L
definition of continuity Answer: f(x) is continuous at x = a if limx->a
f(x) = f(a)
types of discontinuities Answer: removeable (hole in graph), jump
(hole but a point somewhere else), infinite (graph approaches infinity)
intermediate value theorem Answer: if f(x) is continuous on [a, b] and
N is a number in between f(a) and f(b) then somewhere there is a point
c in between a and b such that f(c) = N
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, 2
cosh Answer: (e^x + e^-x)/2
sinh Answer: (e^x - e^-x)/2
derivative of tanx/cotx Answer: sec^2x/-csc^2x
derivative of secx/cscx Answer: secxtanx/-cscxcotx
implicit derivatives Answer: 1) take the derivative of both sides,
treating y as a function of x, 2) solve for dx/dy, result will involve both
x and y
derivative of arcsinx/sin^-1x Answer: 1/(1-x^2)^(1/2)
derivative of arccosx/cos^-1x Answer: -1/(1-x^2)^(1/2)
derivative of arctanx/tan^-1x Answer: 1/(1+x^2)
derivative of arcsecx/sec^-1x Answer: 1/(|x|*(x^2-1)^(1/2))
derivative of logb(x) Answer: 1/xln(b)
derivative of b^x Answer: b^x ln(b)
linearization Answer: L(x) = f(a) + f'(a)(x - a)
hyperbolic function derivatives Answer: know em
© 2025 All rights reserved
APMA 1090 Final Questions with Answers (100% Correct
Answers)
indeterminate forms Answer: when f(x) isn't continuous at c, may
result in 0/0...etc, need to rewrite to solve
difference quotient Answer: f(x+h)-f(x)/h, used to find the slope of the
tangent line
heaviside function Answer: H(x) = {0 x < 0, 1 x >= 0}
squeeze theorem Answer: If f(x) <= g(x) <= h(x) for x near a, and limx-
>a f(x) = limx->a h(x) = L, then limx->a g(x) = L
definition of continuity Answer: f(x) is continuous at x = a if limx->a
f(x) = f(a)
types of discontinuities Answer: removeable (hole in graph), jump
(hole but a point somewhere else), infinite (graph approaches infinity)
intermediate value theorem Answer: if f(x) is continuous on [a, b] and
N is a number in between f(a) and f(b) then somewhere there is a point
c in between a and b such that f(c) = N
© 2025 All rights reserved
, 2
cosh Answer: (e^x + e^-x)/2
sinh Answer: (e^x - e^-x)/2
derivative of tanx/cotx Answer: sec^2x/-csc^2x
derivative of secx/cscx Answer: secxtanx/-cscxcotx
implicit derivatives Answer: 1) take the derivative of both sides,
treating y as a function of x, 2) solve for dx/dy, result will involve both
x and y
derivative of arcsinx/sin^-1x Answer: 1/(1-x^2)^(1/2)
derivative of arccosx/cos^-1x Answer: -1/(1-x^2)^(1/2)
derivative of arctanx/tan^-1x Answer: 1/(1+x^2)
derivative of arcsecx/sec^-1x Answer: 1/(|x|*(x^2-1)^(1/2))
derivative of logb(x) Answer: 1/xln(b)
derivative of b^x Answer: b^x ln(b)
linearization Answer: L(x) = f(a) + f'(a)(x - a)
hyperbolic function derivatives Answer: know em
© 2025 All rights reserved
