Problem Set 3 Partial Solutions
... Z ln 2 e3x f (e3x ) dx, we make the substitution u = e3x . Then Solution: To evaluate ...
... Z ln 2 e3x f (e3x ) dx, we make the substitution u = e3x . Then Solution: To evaluate ...
MTA
... 2. Real analysis : Sequences and series, continuity and differentiability of real valued functions of one variable and applications, uniform convergence, Riemann integration, continuity and differentiability of real valued functions of several variables, partial derivatives and mixed partial derivativ ...
... 2. Real analysis : Sequences and series, continuity and differentiability of real valued functions of one variable and applications, uniform convergence, Riemann integration, continuity and differentiability of real valued functions of several variables, partial derivatives and mixed partial derivativ ...
Copy of exam
... • To find ∆xi , first determine the length of the interval [−4, 2]. If the interval is divided into n equal pieces, what is the length of each piece? • To find a formula for xi , note that xi is ahead of the number −4 by i × the width of one piece. • Here are some of the special sums-of-powers formu ...
... • To find ∆xi , first determine the length of the interval [−4, 2]. If the interval is divided into n equal pieces, what is the length of each piece? • To find a formula for xi , note that xi is ahead of the number −4 by i × the width of one piece. • Here are some of the special sums-of-powers formu ...
Section 1: Factor polynomial equations over the reals (quadratics
... Find second derivatives of polynomial, rational, exponential and log functions using the power rule, product rule, quotient rule, and chain rule Locate local extrema (max and min) of a given function as well as inflection points Locate absolute extrema on a closed interval. Use first and second deri ...
... Find second derivatives of polynomial, rational, exponential and log functions using the power rule, product rule, quotient rule, and chain rule Locate local extrema (max and min) of a given function as well as inflection points Locate absolute extrema on a closed interval. Use first and second deri ...
The Accumulation Function
... The Fundamental Theorem of calculus gives the precise inverse relationship between the derivative and the integral. The statement of the theorem includes the definition of an area so far, or accumulation function. This presentation focuses on the accumulation function, some typical applications, and ...
... The Fundamental Theorem of calculus gives the precise inverse relationship between the derivative and the integral. The statement of the theorem includes the definition of an area so far, or accumulation function. This presentation focuses on the accumulation function, some typical applications, and ...
Integration by inverse substitution
... Common errors to avoid Watch the algebra as you do the substitutions, both ways. Use the triangle model to return to the original variable, rather than constructing convoluted compositions of trig functions and their inverses. ...
... Common errors to avoid Watch the algebra as you do the substitutions, both ways. Use the triangle model to return to the original variable, rather than constructing convoluted compositions of trig functions and their inverses. ...
this document - KSU Web Home
... In practice, …nding A using the de…nition is very di¢ cult. First, the expression resulting from the sum is usually very complicated. Then, we have to take its limit as n approaches in…nity. We will not spend any more time on it, but you should remember the formula. ...
... In practice, …nding A using the de…nition is very di¢ cult. First, the expression resulting from the sum is usually very complicated. Then, we have to take its limit as n approaches in…nity. We will not spend any more time on it, but you should remember the formula. ...
Review 3 MTH132-040, Calculus I (1) Jane is 2 miles offshore in a
... subintervals of length 1 with left-endpoint values. (d) What is an upper estimate of the total population of bacteria on day 4, if there were 100 bacteria on day 1? (9) Find the average temperature for Monday, if the temperature for that day as a function of time t was given by T (t) = 40 + 10 sin(t ...
... subintervals of length 1 with left-endpoint values. (d) What is an upper estimate of the total population of bacteria on day 4, if there were 100 bacteria on day 1? (9) Find the average temperature for Monday, if the temperature for that day as a function of time t was given by T (t) = 40 + 10 sin(t ...
Document
... If the points P and Q have position vectors r(t) and r(t + h), then represents the vector r(t + h) – r(t), which can therefore be regarded as a secant vector. If h > 0, the scalar multiple (1/h)(r(t + h) – r(t)) has the same direction as r(t + h) – r(t). As h 0, it appears that this vector approac ...
... If the points P and Q have position vectors r(t) and r(t + h), then represents the vector r(t + h) – r(t), which can therefore be regarded as a secant vector. If h > 0, the scalar multiple (1/h)(r(t + h) – r(t)) has the same direction as r(t + h) – r(t). As h 0, it appears that this vector approac ...
Math 601 Solutions to Homework 10
... (a) On the circle C, the value of (x2 + y 2 )2 is 34 = 81. If we integrate this function over the circle, we get 81 times the circumference of the circle, which is 81(3)(2π) = 486π (b) The problem should have specified the orientation of C. We will assume that C is oriented counterclockwise. Z We wa ...
... (a) On the circle C, the value of (x2 + y 2 )2 is 34 = 81. If we integrate this function over the circle, we get 81 times the circumference of the circle, which is 81(3)(2π) = 486π (b) The problem should have specified the orientation of C. We will assume that C is oriented counterclockwise. Z We wa ...
3.3 Increasing and Decreasing and the First Derivative Test
... Put the critical numbers you found on a number line (dividing it into regions). Pick a value from each region, plug it into the first derivative and note whether your result is positive or negative. Indicate where the function is increasing or decreasing. ...
... Put the critical numbers you found on a number line (dividing it into regions). Pick a value from each region, plug it into the first derivative and note whether your result is positive or negative. Indicate where the function is increasing or decreasing. ...
What is the Second Fundamental Theorem of Calculus
... Homework Review (10 minutes): Students are assigned problems to present on board. Students will also answer questions. Teacher can go over a problem if no one in class could explain it ...
... Homework Review (10 minutes): Students are assigned problems to present on board. Students will also answer questions. Teacher can go over a problem if no one in class could explain it ...