Calculus Study guides, Class notes & Summaries

Derivative of arcsin(x) - ANSWER-1/sqrt(1-x^2) Derivative of arccos(x) - ANSWER--1/sqrt(1-x^2) derivative of arctan(x) - ANSWER-1/(1+x^2) derivative of arccsc(x) - ANSWER--1/(|x|√(x²-1)) derivative of arcsec(x) - ANSWER-1/(abs(x)sqrt(x^2-1)) derivative of arccot(x) - ANSWER--1/(1+x^2) derivative of sin(x) - ANSWER-cosx derivative of cos(x) - ANSWER--sinx derivatie of tan(x) - ANSWER-sec^2(x) (being this makes you two times more seccy) derivative of csc(x) - ANSWER--...

d sin x - ANSWER-cos x d cos x - ANSWER-- sin x d tan x - ANSWER-sec^2 x ∫sin x - ANSWER-- cos x ∫cos x - ANSWER-sin x ∫ sec^2 x - ANSWER-tan x d ln U - ANSWER-dU / U ∫ e^U dU - ANSWER-e^U ∫ dU / U - ANSWER-ln |U| e^ln x - ANSWER-x ln e^x - ANSWER-x ln e - ANSWER-1 ln 1 - ANSWER-0 ln A^B - ANSWER-B ln A ln (A/B) - ANSWER-ln A - ln B ln AB - ANSWER-ln A + ln B d e^U - ANSWER-e^U dU limit as x approaches 0 in: (sin x)/x - ANSWER-1 lim...

Find all points of relative minima and maxima: y = x^2 + 6x + 5 - ANSWER-minima at (-3, -4) Find all points of relative minima and maxima: y = -12/(x^2 + 3) - ANSWER-minima at (0, -4) Find the open intervals where the function is concave up and concave down. y = (2x-12)^(1/3) - ANSWER-concave up: (-∞, 6) concave down: (6, ∞) Find the open intervals where the function is concave up and concave down. y = -x^3 + x^2 + 3 - ANSWER-concave up: (-∞, 1/3) concave down: (1/...

Derivative of sin(x) - ANSWER-cos(x) Derivative of cos(x) - ANSWER--sin(x) Derivative of tan(x) - ANSWER-sec^2(x) Derivative of sec(x) - ANSWER-sec(x) tan(x) Derivative of cot(x) - ANSWER--csc^2(x) Derivative of csc(x) - ANSWER--csc(x) cot(x) Limits of infinity with highest exponent on top - ANSWER--/+ infinity Limits of infinity with highest exponent on bottom - ANSWER-0 Limits of infinity with same highest exponent - ANSWER-coefficents Tangent lines - ANSWER-slope/ d...

The slope of a secant line represents what kind of change? - ANSWER-Average roc The slope of a tangent line represents what kind of change? - ANSWER-Instantaneous roc What kind of change does an integral represent? - ANSWER-Total change Explain what a derivative is graphically. - ANSWER-Slope of tangent line Explain what a derivative is numerically. - ANSWER-Difference quotient from a table Explain what a derivative is analytically. - ANSWER-lim of (f(x+h)-f(x))/h as h->0 3 ...

Integral of cosx - ANSWER-sinx+c Integral of sin x - ANSWER--cosx+c Integral of sec^2x - ANSWER-tanx+c Integral of secxtanx - ANSWER-secx+c Integral of csc^2x - ANSWER--cotx+c Integral of cscxcotx - ANSWER--cscx+c If a trapezoidal sum overapproximates ∫0 to 4 f(x)dx, and a right Riemann sum underapproximates ∫0 to 4 f(x)dx, which of the following could be the graph of y=f(x)? - ANSWER-A- The one with a y intercept at three that is concave up and decreasing Let f be the f...

Find the limit as x approaches a number. - ANSWER-Plug in the number. If you get 0/0, factor and cancel then plug in again. Find the limit as x approaches infinity. - ANSWER-Degree on top greater -> DNE Degree on bottom greater -> zero Degrees the same -> ratio of leading coefficients L'Hopitals Rule for Limits - ANSWER-Take derivative of top and bottom separately, then plug in number again (repeat until you get an answer, or DNE) Show that f(x) is continuous. - ANSWER-1) Li...

Let g(x)=x^4+4x^3. How many relative extrema does g have? - ANSWER-B. One An object moves along a straight line so that at any time t its acceleration is given by a(t)=6t. At time t=0, the objects velocity is 10 and the position is 7. What is the object's position at t=2? - ANSWER-D. 35 Let g be a continuous function. Using the substitution u=2x-1, the integral from [2, 3] g(2x-1)dx is equal to which of the following? - ANSWER-B. (1/2) integral [2, 3] g(u)du lim from x->3 (tan(x-3))...

what does a function have to be in order for it to have a constant rate of change - ANSWER-linear what is slope intercept form - ANSWER-y=mx+b whats the equation of a line - ANSWER-y-y initial=m(x-x initial) in a problem showing attendance at NFL games over the years, what will the average rate of change formula look like - ANSWER-change in attendance/ change in time in a problem talking about an increase in town population, what will the formula for relative rate of change look like...

Read the following three statements A, B and C. Based on the statements A, B and C, given above, which one of the following is correct? - ANSWER-C. If f'(x) > 0 in (a,b) and f"(x) < 0 in (a,b), then the graph of f(x) is decreasing AND concave down in (a,b). C. The Statements A and B are true Find dy/dx by implicit differentiation of x^3 - xy + y^2 = 4 and evaluate dy/dx at (0,-2) - ANSWER-C. dy/dx = y-3x^2/ 2y-x; dy/dx at (0,-2) = 1/2 The radius r of a circle is increasing ...