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Class: MATH 75 - Calculus I; Subject: Mathematics; University: California State University - Fresno; Term: Spring 2015;
Typology: Quizzes
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function cannot cross a vertical line more than once TERM 2
DEFINITION 2 union sign means set is togetherex: 1/x graph the domain would have a U because small gap where not continuous but set still together TERM 3
DEFINITION 3 =1anything to the zero power becomes one TERM 4
DEFINITION 4 the derivative of f(x) with respect to x is the function f^t (x) defined as rise/run <--> f^t (x) = f (x+h) - f(x)/ h TERM 5
DEFINITION 5 use them when there is a pointex: greater than or equal toLess than or greater than would use ( )
is finding where a function is heading"as i approach x from the (left - or right + ) my y values are..." TERM 7
DEFINITION 7 y = mx +bm is slope TERM 8
DEFINITION 8 highest value graph actually hits TERM 9
DEFINITION 9 lowest value graph actually hits TERM 10
DEFINITION 10 sin(theta) = y/rcos(theta) = x/rtan(theta = y/x
f(x) is continuous at x=a if the lim f(x) = f(a) x->a TERM 17
DEFINITION 17 a) a polynomial is continuous everywhereb) a rational function is continuous at every point where the denominator is not zero, and is discontinuous where the points at the denominator equal zero TERM 18
DEFINITION 18
DEFINITION 19 = 1 TERM 20
DEFINITION 20 when limit heading to infinity x/x =1 when x not equal to zero lim x-> infinity
d/dx ( x^n ) = n * x^n -1put exponent in front, subtract one from exponent TERM 22
DEFINITION 22 is the slope of the tangent line TERM 23
DEFINITION 23 d/dx( f * g)^1 = f(x) g1(x) + f1(x) g(x)note: product rule is used to find the derivatives if it is a product (being multiplied)always find f prime and g prime first TERM 24
DEFINITION 24 is a derivative of the first derivative (so take a derivative of whole thing, then take a derivative of what you took a derivative of) TERM 25
DEFINITION 25 f^1 (a) = lim f(x)- f(a)/ x-a x->a = lim f(a+h) - f(a)/h n->0 = m tan (slope of a tangent line)
used when there is a composition (something multiplied by something else) y^1 = f^1 (g(x)) * g^1(x)translatedy^1 = (derivative of the outside function) multiplied by the (derivative of inside function)