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APMA 1090 Final Questions and Answers
(100% Correct Answers) Already Graded A+
indeterminate forms Ans: when f(x) isn't continuous at c, may result in
0/0...etc, need to rewrite to solve
difference quotient Ans: f(x+h)-f(x)/h, used to find the slope of the
tangent line
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heaviside function Ans: H(x) = {0 x < 0, 1 x >= 0}
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squeeze theorem Ans: 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 Ans: f(x) is continuous at x = a if limx->a f(x) = f(a)
types of discontinuities Ans: removeable (hole in graph), jump (hole but
a point somewhere else), infinite (graph approaches infinity)
intermediate value theorem Ans: 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
cosh Ans: (e^x + e^-x)/2
sinh Ans: (e^x - e^-x)/2
derivative of tanx/cotx Ans: sec^2x/-csc^2x
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derivative of secx/cscx Ans: secxtanx/-cscxcotx
implicit derivatives Ans: 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 Ans: 1/(1-x^2)^(1/2)
derivative of arccosx/cos^-1x Ans: -1/(1-x^2)^(1/2)
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derivative of arctanx/tan^-1x Ans: 1/(1+x^2)
derivative of arcsecx/sec^-1x Ans: 1/(|x|*(x^2-1)^(1/2))
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derivative of logb(x) Ans: 1/xln(b)
derivative of b^x Ans: b^x ln(b)
linearization Ans: L(x) = f(a) + f'(a)(x - a)
hyperbolic function derivatives Ans: know em
Fermat's Theorem Ans: if there is a local min or max at x = c, and f'(c)
exists then f'(c) = 0, this does not work the other way around
absolute mins and maxes Ans: occur at end points and critical numbers
critical numbers Ans: where f'(c) = 0 or does not exist
1
APMA 1090 Final Questions and Answers
(100% Correct Answers) Already Graded A+
indeterminate forms Ans: when f(x) isn't continuous at c, may result in
0/0...etc, need to rewrite to solve
difference quotient Ans: f(x+h)-f(x)/h, used to find the slope of the
tangent line
© 2026 Assignment Expert
heaviside function Ans: H(x) = {0 x < 0, 1 x >= 0}
Guru01 - Stuvia
squeeze theorem Ans: 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 Ans: f(x) is continuous at x = a if limx->a f(x) = f(a)
types of discontinuities Ans: removeable (hole in graph), jump (hole but
a point somewhere else), infinite (graph approaches infinity)
intermediate value theorem Ans: 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
cosh Ans: (e^x + e^-x)/2
sinh Ans: (e^x - e^-x)/2
derivative of tanx/cotx Ans: sec^2x/-csc^2x
, For Expert help and assignment handling,
2
derivative of secx/cscx Ans: secxtanx/-cscxcotx
implicit derivatives Ans: 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 Ans: 1/(1-x^2)^(1/2)
derivative of arccosx/cos^-1x Ans: -1/(1-x^2)^(1/2)
© 2026 Assignment Expert
derivative of arctanx/tan^-1x Ans: 1/(1+x^2)
derivative of arcsecx/sec^-1x Ans: 1/(|x|*(x^2-1)^(1/2))
Guru01 - Stuvia
derivative of logb(x) Ans: 1/xln(b)
derivative of b^x Ans: b^x ln(b)
linearization Ans: L(x) = f(a) + f'(a)(x - a)
hyperbolic function derivatives Ans: know em
Fermat's Theorem Ans: if there is a local min or max at x = c, and f'(c)
exists then f'(c) = 0, this does not work the other way around
absolute mins and maxes Ans: occur at end points and critical numbers
critical numbers Ans: where f'(c) = 0 or does not exist
