Samenvattingen, Aantekeningen en Examens

volume equation - ANSWER-v=4/3 r^3 related rate problems - ANSWER-treat all variables as functions of time, use implicit differentiation to produce equalities which can be solved for the desired rates linear approximation equation - ANSWER-f'(a)(x-a)+f(a) linear approximation - ANSWER-approximating functions using the equation of a line, also known as tangent line approxiamtion equation for dy - ANSWER-f'(x)dx or f'(x)delta x dy - ANSWER-differential, dependent on both the valu...

INTG(sin(x) dx) - ANSWER--cos(x) + C INTG(cos(x) dx) - ANSWER-sin(x) + C INTG((sec(x))^2 dx) - ANSWER-tan(x) + C INTG((csc(x))^2 dx) - ANSWER--cot(x) + C INTG(sec(x)*tan(x) dx) - ANSWER-sec(x) + C INTG(csc(x)*cot(x) dx) - ANSWER--csc(x) + C INTG(b^x dx) - ANSWER-(1/ln(b))*b^x + C INTG(1/x dx) - ANSWER-ln(abs(x)) + C INTG((1/sqrt(1-x^2)) dx) - ANSWER-arcsin(x) + C INTG(-(1/sqrt(1-x^2)) dx) - ANSWER-arccos(x) + C INTG((1/(1+x^2)) dx) - ANSWER-arctan(x) + C Rational...

∫ 2x / (x² - 1) - ANSWER-Method: U sub HW 6 #1 Answer: ln(x+1) + ln(x-1) + C ∫ x - 8 x² + 2x - 8 - ANSWER-Method: Partial Fractions HW 6 #3 Answer: 2 ln(x+4) - ln(x-2) + C ∫ 9x - 25 3x² - 13x + 4 - ANSWER-Method: Partial Fractions HW 6 #5 Answer: 2 ln(3x-1) + ln(x-4) + C ∫ x² + 4x + 5 x³ + x² + x + 1 - ANSWER-Method: Partial Fractions HW 6 #7 Answer: 4 tan⁻¹(x) + ln(x+1) + C ∫ 4x² + 11 x³ + x² + 4x + 4 - ANSWER-Method: Partial Fractions HW 6 #9 An...

Vertical Asymptote - ANSWER-Set Denominator equal to zero Horizontal asymptote - ANSWER-set numerator equal to zero Rolles theorem states there is... - ANSWER-a tangent line at some point on a closed interval [a,b] if the following hold true a) continuous b) differentiable c) f(a)=f(b) Integration is a... - ANSWER-continuous addition process Intermediate Value Theorem: Suppose f is a function continuous at every point on the interval [a,b]: - ANSWER-a) f will take on every value b...

evaluate the integral 2/1, ln(x)/x dx - ANSWER-(ln2)^2/2 consider the function f(x)=x^4-4x^3. which of the following is NOT true - ANSWER-f has a local extrema at x=0 and x=3 find the work done by a force F=sqroot 2x+1 N to move an object along a straight path from a distance of 0 meters to a distance of 4 meters - ANSWER-26/3 J an object is moving along the x-axis. Let s(t), v(t) and a(t) be functions giving the position, the velocity, and the acceleration of the object at time t. whic...

Section 1.2 What is point-slope form? - ANSWER-y-y1=m(x-x1) Section 1.3 What is the average rate of change? How do you find it? - ANSWER-The average rate of change is the slop of the function between any two times. You find it by solving for the slope. Section 1.3 What is relative rate of change? How do you find it? - ANSWER-Relative change is usually expressed as a percentage with no unit. You can find it by using the equation (p1-p0)/(p0). Section 1.3 How do you know if something is c...

evaluate the integral 2/1, ln(x)/x dx - ANSWER-(ln2)^2/2 consider the function f(x)=x^4-4x^3. which of the following is NOT true - ANSWER-f has a local extrema at x=0 and x=3 find the work done by a force F=sqroot 2x+1 N to move an object along a straight path from a distance of 0 meters to a distance of 4 meters - ANSWER-26/3 J an object is moving along the x-axis. Let s(t), v(t) and a(t) be functions giving the position, the velocity, and the acceleration of the object at time t. whic...

Section 1.2 What is point-slope form? - ANSWER-y-y1=m(x-x1) Section 1.3 What is the average rate of change? How do you find it? - ANSWER-The average rate of change is the slop of the function between any two times. You find it by solving for the slope. Section 1.3 What is relative rate of change? How do you find it? - ANSWER-Relative change is usually expressed as a percentage with no unit. You can find it by using the equation (p1-p0)/(p0). Section 1.3 How do you know if something is c...

True or False: f(x)= (1/3)x^3 - x^2 - 3x +1 has two critical numbers - ANSWER-False x= -1 Find the number of critical numbers for f(x)= (cosx)^2- sinx on [0, 2pi] - ANSWER-4 critical numbers: x= pi/2, 7pi/6, 3pi/2, 11pi/6 Find the absolute maximum value of f(x)= sinx on [-pi/3, pi/4] - ANSWER-absolute maximum: 1/sqrt(2) Fins all of the critical numbers for f(x)= sqrt(x^2 - 4) - ANSWER-no critical numbers True or False The hypotheses of the Mean Value Theorem are satisfied for f(x...

Power Rule - ANSWER-Example: y=x^67, y'=67x^66 Constant Multiple Rule - ANSWER-Examples: y=7x^8, y'=7(8)x^7 Sum Rule - ANSWER- IF y=e^x then y'=e^x - ANSWER-IF y=e^x then y'=e^x Product rule - ANSWER-_____ x ______ + ______ x ______ Quotient Rule - ANSWER-HoDiHi - HiDiHo/ Ho^2 derivative of sin - ANSWER-cosx derivative of cosx - ANSWER--sinx derivative of tan - ANSWER-sec^2x ( x not with exponent) Chain rule - ANSWER-example: f(x): (x^2+2x-3)^10 f(x)'= 10(x^2 +2x-...