MATH 2B Study Guide - Midterm Guide: Blood Type, Intermediate Value Theorem, Exponential Function

Math 1510 Preview A.14: Analysis Objective There are many situations where functions arise as area functions for some continuous integrand, that is F(x)- 0) d In this activity you will use the tools of calculus to analyze such a function. Background If the integrand(r) has an elementary antiderivative then the second part of the Fundamentall Theorenm of Calculus gives a formula for the area function F(x). However, many functions do not have an elementary antiderivative. In such a situation we can use the first part of the Fundamental Theorem to get information about F through its derivative. You should review section 5.3 and make sure you understand both parts of the Fundamental Theorem. You will also want to use a CAS (for example Wolfram Alpha) for some of your computations. CAUTION: Some systems (including Alpha) will report an antiderivative for the integral below but they are not useful in this problem because they incorporate assumptions that are not valid here. For calculating numeric estimates of area using the midpoint rule you may use the Desmos example The Midpoint Rule Steps: You will analyze the function sin ()+1 1. Domains. Describe the domains of the area function F(x) and the integrand s). 2. Values. Use the midpoint rule to estimate the following values: 6 F(x) 3. Symmetry. Does F(x) have any properties such as symmetry (even or odd) or periodicity? Page 1 of 2

Math 1510 Preview A.14: Analysis Objective: There are many situations where functions arise as area functions for some continuous integrand, that is F(x)- ro) d In this activity you will use the tools of calculus to analyze such a function. Background: If the integrand f(t) has an elementary antiderivative then the second part of the Fundamental Theorem of Calculus gives a formula for the area function F(x). However, many functions do not have an elementary antiderivative. In such a situation we can use the first part of the Fundamental Theorem to get information about F through its derivative. You should review section 5.3 and make sure you understand both parts of the Fundamental Theorem. You will also want to use a CAS (for example Wolfram Alphal for some of your computations. CAUTION: Some systems (including Alpha) will report an antiderivative for the integral below but they are not useful in this problem because they incorporate assumptions that are not valid here. For calculating numeric estimates of area using the midpoint rule you may use the Desmos example The Midpoint Rule Steps: You will analyze the function 8 cos(e)+v 1. Domains. Describe the domains of the area function F(x) and the integrand() 2. Values. Use the midpoint rule to estimate the following values 4 3. Symmetry. Does P(x) have any properties such as symmetry leven or odd) or periodicity Page 1 of 2

Determine the end behavior of the following function as x → +oo and as X →-00. f(x) = 5x-4 As x → +00,f(x) → Equation Editor | sin (a) x/ 血Help -00 As X → -00,f(x) → Equation Editor d' sin (a) Help -00

XYour answer is incorrect. Try again. Link to question with no attempts available What families does the function 1(x) = Assume a, b and c are positive constants. Select all that apply. ( )" belong to? Power Rational O Exponential Polynomial

Assume/x) is continuous on an interval around x = 0, except possibly at x = 0. What does the table of values suggest as the integer value of lim f(x)? x 1-0. I -0.01 | 0.01 | 0.1 ТР8.987P8.999|98.999 8.987 lim f(x) seems to be equal to 99 Does the limit definitely have this value? Select all the options that apply Yes, because the function is continuous on an interval around x = 0. Yes, the table shows this is the limit with certainty O No, we do not know the limit or sure because for values of χ c se to 0 different from those the table the va a eso c m ght not approach the given value. O No, the limit may not exist, even though the table seems to hint it does No, the function could be approaching, for example, 99.00001 or 98.9999 Yes, the table indicates that for values of x close to O different from those in the table, the values of f(x) will approach the given value.

Chapter 1, Section 1.5, Question 020 Your answer is incorrect. Try again. Find a possible formula for the graph -20 π 20π Enclose arguments of functions in parentheses. For example, sin (2x) f(x)=1 6-sin(pix/10)