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Formulas to know MATH 100, Exams of Advanced Education

Abilene Christian University (ACU)Advanced Education

Formulas to know MATH 100---------

Typology: Exams

2025/2026

Available from 02/13/2026

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Formulas to know MATH 100
sin^-1(x) - correct answer 1/sqrt(1-u^2) * du/dx
cos^-1(x) - correct answer -1/sqrt(1-u^2) • du/dx
tan^-1(x) - correct answer 1/(u^2+1) * du/dx
cot^-1(x) - correct answer -1/(1+u^2) * du/dx
sec^-1(x) - correct answer 1/(abs(x)sqrt(u^2-1)) * du/dx
csc^-1(x) - correct answer -1/(abs(x)sqrt(x^2-1)) * du/dx
volume of cone - correct answer V = 1/3πr²h
volume of sphere - correct answer V = 4/3πr³
Area of sphere - correct answer V = 4πr^2
Area of a parallelogram - correct answer A=bh
Area of a trapezoid - correct answer A=1/2h(b1+b2)
Volume of any cylinder with identical bases - correct answer V = area of base x h
Area of cone - correct answer A = πrl+πr^2
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Formulas to know MATH 100

sin^-1(x) - correct answer 1/sqrt(1-u^2) * du/dx cos^-1(x) - correct answer -1/sqrt(1-u^2) • du/dx tan^-1(x) - correct answer 1/(u^2+1) * du/dx cot^-1(x) - correct answer -1/(1+u^2) * du/dx sec^-1(x) - correct answer 1/(abs(x)sqrt(u^2-1)) * du/dx csc^-1(x) - correct answer -1/(abs(x)sqrt(x^2-1)) * du/dx volume of cone - correct answer V = 1/3πr²h volume of sphere - correct answer V = 4/3πr³ Area of sphere - correct answer V = 4πr^ Area of a parallelogram - correct answer A=bh Area of a trapezoid - correct answer A=1/2h(b1+b2) Volume of any cylinder with identical bases - correct answer V = area of base x h Area of cone - correct answer A = πrl+πr^

sin(a+b) - correct answer sinAcosB+cosAsinB sin(a-b) - correct answer sinAcosB-cosAsinB cos(a+b) - correct answer cosAcosB-sinAsinB cos(a-b) - correct answer cosAcosB+sinAsinB Inverse Derivative - correct answer (f^-1)'(x) = 1/f'(f^-1(x)) sec/tan identity - correct answer sec^2(x) = 1 + tan^2(x) sec^-1(x) identity - correct answer cos^-1(1/x) csc^-1(x) identity - correct answer sin^-1(1/x) cot^-1(x) identity - correct answer tan^-1(1/x) differentiation change in f (true change) - correct answer delta f = f(x0 + dx) - f(x0) estimate of change - correct answer df = f'(x0)dx approx error - correct answer error = I delta f - df I Derivative of a^x - correct answer a^x ln(a) du/da Derivative of Absolute Value - correct answer x/|x| Derivative of loga(x) - correct answer 1/xlna du/dx

jerk is derivative of acceleration average value of a function - correct answer 1/b-a (integral a-b) f(x)dx sum of first n integers - correct answer n(n+1)/ sum of first n squares - correct answer n(n+1)(2n+1)/ sum of first n cubes - correct answer (n(n+1)^/2)^ formula of Riemann sums - correct answer (standard sigma notation) f(ck)deltax ck = a+k(b-a)/n delta x = b-a/n Right Hand Riemann Sum - correct answer uses right point in kth subinterval left hand riemann sum - correct answer uses left point in kth subinterval Midpoint Riemann Sum - correct answer uses middle value in kth subinterval Definition of Definite Integral - correct answer lim n -> infinity (standard sigma notation) f(x*) delta x often take lim n-> n of riemann sum formula formula for riemann sums of equal width subintervals - correct answer lim n -> infinity (standard sigma notation) f(a+k(b-a/n))(b-a/n) Max-Min Inequality for integrals - correct answer if f has a max and min value on [a,b] then min(f)(b-a) is less than the integral of f(x) from a to b, which is less than the max(f)(b-a)

Fundamental Theorem of Calculus part 1 - correct answer F'(x) = d/dx integral from a to x f(t)dt = f(x) how to find derivative of integral (FTC 1) directly - correct answer plug in upper limit for dummy variable, and times expression by derivative of upper limit fundamental theorem of calculus part 2 - correct answer ∫ f(x) dx on interval a to b = F(b) - F(a) trapezoid rule - correct answer T = deltax/2 (y0 +2y1 + 2y2+ ... + 2yn-1 +yn) simpson's rule - correct answer S = deltax/3 (y0 + 4y1 +2y2 + 4y3 + ... + 4yn- +yn) IMPORTANT: NEED EVEN NUMBER INTERVALS area between curves - correct answer A=∫f(x)-g(x) dx is f is even, then integral from [-a, a] - correct answer is 2 times integral from [-a, a] if f is odd, then integral from [-a, a] - correct answer is 0 from [-a, a] integration with respect to y - correct answer A = ∫c to d of (f(y) - g(y)) dy sin^2 x identity = - correct answer (1-cos2x)/ cos^2(x) identity - correct answer (1+cos2x)/ even function - correct answer f(-x)=f(x) odd function - correct answer f(-x)=-f(x)