Calculus 1 Final Exam
Study online at https://quizlet.com/_g6tace
1. Continuity a function is continuous if:
1. f(a) is difined (a is the domain of f)
2. lim f(x) as x approaches a exists
3. f(x) = f(a)
2. Extreme Value if f is contunous on a closed interval [a,b] then f attains any
Theorum value between f(a) and f(b)
3. Newtons Method - xn+1 = xn - f(xn)/f'(xn) untill the difrance is substantially
small
- used to approximate the root of a function
- on a graph your initial guess will make a tangent line,
and using newtons method tangent lines keep being made
untill theyre closer
4. derivitive of a - f(a+h) - f(a)/h
funtion
5. diferentibility cri- - a corner or kink
teria - discontinuty
- vertical tangent line
6. triginomic derivi- - sin = cos
tives basics - cos = -sin
- tan = sec^2
- csc = -csccot
- sec = sectan
- cot = -csc^2
7. derivitive of b^x b^(x)lnb
8. derivitive of g'(x)/g(x)
ln(g(x))
9. derivitive of - 1/f'(f^-1(x))
f^(-1)(x)
10. derivvitive of in- - sin^-1 = 1/sqrt(1-x^2)
verse trig func- - cos^-1 = -1/sqrt(1-x^2)
tions - tan^-1 = 1/1+x^2
1/4
Study online at https://quizlet.com/_g6tace
1. Continuity a function is continuous if:
1. f(a) is difined (a is the domain of f)
2. lim f(x) as x approaches a exists
3. f(x) = f(a)
2. Extreme Value if f is contunous on a closed interval [a,b] then f attains any
Theorum value between f(a) and f(b)
3. Newtons Method - xn+1 = xn - f(xn)/f'(xn) untill the difrance is substantially
small
- used to approximate the root of a function
- on a graph your initial guess will make a tangent line,
and using newtons method tangent lines keep being made
untill theyre closer
4. derivitive of a - f(a+h) - f(a)/h
funtion
5. diferentibility cri- - a corner or kink
teria - discontinuty
- vertical tangent line
6. triginomic derivi- - sin = cos
tives basics - cos = -sin
- tan = sec^2
- csc = -csccot
- sec = sectan
- cot = -csc^2
7. derivitive of b^x b^(x)lnb
8. derivitive of g'(x)/g(x)
ln(g(x))
9. derivitive of - 1/f'(f^-1(x))
f^(-1)(x)
10. derivvitive of in- - sin^-1 = 1/sqrt(1-x^2)
verse trig func- - cos^-1 = -1/sqrt(1-x^2)
tions - tan^-1 = 1/1+x^2
1/4
