Study guides, Class notes & Summaries

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 ...

power rule - ANSWER-if y = x^k -- then, k * x^k⁻¹ product rule - ANSWER-f(x) • g(x) then [f(x)•g(x)' + f(x)'•g(x)] quotient rule - ANSWER-D(x) • N'(x) - N(x) •D'(x) --------------------- [D(x)]² extended power rule - ANSWER-[g(x)]^k = k[g(x)]^k-1 • g(x)' chain rule - ANSWER-[f of g(x)]' = [f(g(x))]' = f'(g(x)) • g'(x) high order derivatives - ANSWER- what does a second derivative represent? - ANSWER-the rate of change of the rate of change ...

equation of a tangent line - ANSWER-y= f'(x)(x-x1)+f(x) difference quotient/ average rate of change (AROC) - ANSWER-f(x+h)-f(x)/h point slope form of a line - ANSWER-y-y1=m(x-x1) derivative is the same as... - ANSWER--slope of the tangent line -instantaneous rate of change -marginal (cost, profit, revenue) slope of the secant line - ANSWER-msec= (y2-y1)/(x2-x1) constant rule - ANSWER-if C is a real number, then the derivative of C =0 power rule - ANSWER-if n is a nonnegative...

Points of Inflection - ANSWER-If (c, f(c)) is a point of inflection of the graph of f, then either f"(c)=0 or f" is undefined at c Critical Value - ANSWER-Where first derivative is 0 or undefined Find absolute extrema - ANSWER-Use critical values and END POINTS in the function Horizontal Asymptote Rules - ANSWER-If m>n: NO HA If m=n: HA = co-eff of m/co-eff of n If m<n: HA: y = 0 Mean Value Theorem - ANSWER-if f(x) is continuous on [a,b] and differentiable on (a,b), there i...

definition of a limit - ANSWER-A limit is a number that a function approaches as x approaches a value Limit equation - ANSWER-f(x+h)-f(x)/h e ln(x) - ANSWER-x e^x e^y - ANSWER-e^(x+y) e^xy - ANSWER-(e^x)^y lne^x - ANSWER-x ln(xy) - ANSWER-ln(x)+ln(y) ln(x^y ) - ANSWER-ylnx tan theta - ANSWER-sin theta/cos theta secant of theta - ANSWER-1/cos theta cot theta - ANSWER-cos theta/sin theta csc theta - ANSWER-1/sin theta lim x->c (f(x) + g(x)) - ANSWER-lim x-&gt...

What will calculus enable you to do? - ANSWER-Find the volumes of oddly shaped objects Consider the function y=x^2-2x+1. What is the slope of the tangent line at x=2? - ANSWER-2 What is the average rate of change of the function y=2x^2+3 between x=x1 and x=x2 - ANSWER-2(x2+X1) What is the slope of the secant line of the function y=4x^2-2x+1 between x=3 and x=6 - ANSWER-34 A body is thrown upward so that its height h at the end of t seconds is h=160t-16t^2. What is its max height? - A...

Power Rule - ANSWER-d/dx x^n = nx^n-1 d/dx [c] - ANSWER-0 d/dx [sinx] - ANSWER-cosx d/dx [cosx] - ANSWER--sinx d/dx [e^x] - ANSWER-e^x Product Rule - ANSWER-d/dx [f(x) g(x)] = f'g+g'f Quotient Rule - ANSWER-d/dx [f(x)/g(x)] = f'g-g'f/g^2 d/dx [tanx] - ANSWER-sec^2x d/dx [secx] - ANSWER-secxtanx d/dx [cotx] - ANSWER--csc^2x d/dx [cscx] - ANSWER--cscxcotx Chain Rule - ANSWER-d/dx [f(g(x))] = f'(g(x)) * g'(x) Inside/Outside Properties - ANSWER-y=(inside)^n ...