Calculus Study guides, Class notes & Summaries

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-...

What is the difference quotient? - ANSWER-f(x+h)-(f(x) _______________ h Lim f(x) = 4 x > 2 - ANSWER-As x approaches 2, y is very close to 4 Lim f(x) = 2 x > 2 - ANSWER-As x approaches 2, y is either undef. or = to 4 Does the limit exist? Lim f(x) = 4 x > 2 - ANSWER- Lim x^2 - 9 ________ x > 3 x - 3 - ANSWER-Step 1: (x-3)(x+3) _____________ x-3 Step 2: (cross out)(x+3) ______________________ cross out Step 3: x+3 Step 4: 3 What is the de...

Average Rate of Change - ANSWER-Slope of two points Instantaneous Rate of Change - ANSWER-Derivative Derivative is - ANSWER-the slope of the tangent line at one point Mean Value Theorem - ANSWER-If a function is both continuous and differentiable on an interval, then there exists some 'c' in that interval at which the average rate of change equals the instantaneous rate of change Normal line - ANSWER-Perpendicular to a tangent line Definition of Derivative - ANSWER-The limit as ...

What can be used to determine whether a relation satisfies the definition of a function? - ANSWER-Vertical Line Test What are the four ways a function can be represented? - ANSWER-numerically, algebraically, verbally, graphically What must be met in order to be considered a function (basic level here) - ANSWER-one output for every input A table of data is a ____ representation of a function - ANSWER-numerical A scatterplot is a ____ representation of a function - ANSWER-graphical ...

Constant Rule - ANSWER-d/dx [c] = 0 Constant Multiple Rule - ANSWER-d/dx [cf(x)]=cf'(x) Sum Rule - ANSWER-d/dx [f(x)+g(x)] = f'(x)+g'(x) Difference Rule - ANSWER-d/dx [f(x)-g(x)] = f'(x)-g'(x) Product Rule - ANSWER-d/dx [f(x)*g(x)] = f(x)g'(x) + f'(x)g(x) Quotient Rule - ANSWER-d/dx [f(x)/g(x)] = [g(x)f'(x) - g'(x)f(x)]/[g(x)²] Chain Rule - ANSWER-d/dx [f(g(x)] = f'(g(x))*g'(x) Power Rule - ANSWER-d/dx[xⁿ]=nxⁿ⁻¹ Definition of the number e - ANSWER-d/dx[...