MAT 302 Calculus

MAT 302 Assignment ProblemTrigonometric Integrals | Borough of Manhattan Community CollegeTrigonometric IntegralsQuestion 1(1 point) Evaluate∫sin3xcos5xdx.Question 2(1 point) Evaluate∫tan7xsec2xdx.Question 3(1 point) Evaluate∫tan2(6x)sec4(6x)dx.Question 4(1 point) Evaluate∫sin7xcos3xdx.Question 5(1 point) Evaluate∫tan3tcos3tdt.Question 6(1 point) Evaluate∫tan2(3x)dx.Question 7Question 8(1 point)Evaluate the integral∫4tan2(x)dxQuestion 9(1 p

15 Mathematics Assignment Help / Calculus Borough of Manhattan Community College / MAT 302 19 Jun 2021

MAT 302 Assignment Problem Natural Log Functions Integration | Borough of Manhattan Community CollegeQuestion 1(1 point) Evaluate the indefinite integral. ∫x+2x2+4x+5dxQuestion 2(1 point) Find the following integral. Note that you can check your answer by differentiation.Question 3(1 point) Find the following integral. Note that you can check your answer by differentiation.Question 4(1 point) Evaluate the indefinite integral. ∫4dxxl

11 Mathematics Assignment Help / Calculus Borough of Manhattan Community College / MAT 302 19 Jun 2021

MAT 302 Assignment Problem Area of Region Between Two Curves | Borough of Manhattan Community CollegeArea of Region Between Two CurvesQuestion 1(1 point) Find the area of the region that is enclosed betweeny=11x2−x3+xy=11x2−x3+xandy=x2+25xy=x2+25x.Question 2(1 point) Find the area of the region enclosed by the two functionsy=5x2y=5x2andy=x2+4.y=x2+4.Question 3(1 point)Find the area of the region between the curvesy=12−x2y=12−x2andy=x2−6.Ques

12 Mathematics Assignment Help / Calculus Borough of Manhattan Community College / MAT 302 19 Jun 2021

MAT 302 Assignment Problem 9.10 |Borough of Manhattan Community College9.10 Taylor and Maclaurin SeriesQuestion 1(1 point) Match each of the Maclaurin series with the function it represents.Question 2(1 point) Match each of the Maclaurin series with correct function.Question 3(1 point) Find the first five non-zero terms of Taylor series centered atx=10x=10for the function below.f(x)=lnxQuestion 4(1 point) Find the first five non-zero terms of Mac

12 Mathematics Assignment Help / Calculus Borough of Manhattan Community College / MAT 302 19 Jun 2021

MAT 302 Assignment Problem 9.9 | Borough of Manhattan Community College9.9 Representation Of Functions By Power SeriesQuestion 1Use the partial fractions method to express the function as a power series (centered atx=0x=0) and then give the open interval of convergence.Question 2Use differentiation and/or integration to express the following function as a power series (centered atx=0x=0).Question 3Starting with the geometric series∑n=0∞xn∑n=0∞xn,

6 Mathematics Assignment Help / Calculus Borough of Manhattan Community College / MAT 302 19 Jun 2021

MAT 302 Assignment Problem 9.8 |Borough of Manhattan Community College9.8 Power SeriesQuestion 1Consider the power seriesFind the radius of convergenceR.R.If it is infinite, type "infinity" or "inf".Question 2Consider the power seriesFind the radius of convergenceR.R.If it is infinite, type "infinity" or "inf".Question 3Consider the power seriesFind the radius of convergenceR.R.If it is infinite, type "infinity" or "inf".Question 4Consider the po

12 Mathematics Assignment Help / Calculus Borough of Manhattan Community College / MAT 302 19 Jun 2021

MAT 302 Assignmrnent Problem 9.7 |Borough of Manhattan Community College9.7 Taylor Polynomials And ApproximationsQuestion 1ComputeT2(x)T2(x)atx=1x=1fory=exy=exand use a calculator to compute the error|ex−T2(x)||ex−T2(x)|atx=1.4x=1.4.Question 2Calculate the Taylor polynomialsT2(x)T2(x)andT3(x)T3(x)centered atx=πx=πforf(x)=sin(x)f(x)=sin(x). T2(x)T2(x)must be of the formA+B(x−π)+C(x−π)2Question 3(1 point) Write the Taylor polynomialT5(x)T5(x)for th

8 Mathematics Assignment Help / Calculus Borough of Manhattan Community College / MAT 302 19 Jun 2021

MAT 302 Assignment Problem 9.6 | Borough of Manhattan Community College9.6 The Ratio and Root TestQuestion 1(1 point) What can you say about the series∑an∑anin each of the following cases using the Ratio Test? Answer "Convergent," "Divergent," or "Inconclusive."Question 2(1 point) Use the ratio test to determine whetherconverges or diverges.(a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. Forn≥7n≥7,(b)Eval

15 Mathematics Assignment Help / Calculus Borough of Manhattan Community College / MAT 302 19 Jun 2021

MAT 302 Assignment Problem 9.5 | Borough of Manhattan Community College9.5 Alternating SeriesQuestion 1(1 point) Write the general formula for the following alternating series in the form Question 2(1 point) Determine whether the following series converges or diverges. Note:You have only one chance to enter your answer.Question 3(1 point) Determine whether the following series converges or diverges. Note:You have only one chance to enter your

8 Mathematics Assignment Help / Calculus Borough of Manhattan Community College / MAT 302 19 Jun 2021

MAT 302 Assignment Problem 9.4 |Borough of Manhattan Community College9.4 Comparisons of SeriesQuestion 1(1 point) Use the limit comparison test to determine whetherconverges or diverges.(a) Choose a series∑n=13∞bn∑n=13∞bnwith terms of the formbn=1npbn=1npand apply the limit comparison test.Write your answer as a fully simplifiedfraction.Forn≥13n≥13,(b) (b) Evaluate the limit in the previous part. Enter∞∞asinfinityand−∞−∞as-infinity.If the limit

15 Mathematics Assignment Help / Calculus Borough of Manhattan Community College / MAT 302 19 Jun 2021