2012_FALL_MATH1013.ttian.Homework-6 - Math1013 Calculus I Fall 2012 Homework-6 Due at 11:50pm HKT Name Tian TIAN This homework set covers the basics of

2012_FALL_MATH1013.ttian.Homework-6 - Math1013 Calculus I...

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Math1013 Calculus I, Fall 2012 Name: Tian TIAN Homework-6 : Due 12/07/2012 at 11:50pm HKT This homework set covers the basics of antiderivatives (indefinite integrals) and initial value problems, Riemann sums and definite integrals, Fundamental Theorem of Calculus, and the Substitution Rule. 2. Riemann sums are just sum of +ve/-ve rectangular area over subinter-vals, which lead to definite integrals by limit considerations. 3. Fundamental Theorem of Calculus: 4. Substitution rule: turning a complicated integralZg(u)duby an appropriate choice of substitution:u=g(x),du=g0(x)dx.Give 4 or 5 significant digits for numerical answers.For most problemswhen entering numerical answers, you can if you wish enter elementary expres-sions such as 32 or 3**2 instead of 9, sin(3*pi/2)instead of -1,e(ln(3))instead of 3,(1+tan(3))*(4-sin(5))6-15/8 instead of 12748.8657, etc.1.(4 pts)Find the derivative off(x) =-x2+99x+Cto complete thefollowing integration formula:Rdx=-x2+9 Answer(s) submitted: (incorrect) 2.(6 pts) Calculate the following antiderivatives:(a)Z8t-5t3+9dt=+C.(b)Z1u5/4+5.5udu=+C.(c)Z15x3dx=+C. Answer(s) submitted: 3.(6 pts) Calculate the following antiderivatives: Answer(s) submitted: (incorrect) 4.(4 pts) A particle is moving with accelerationa(t) =12t+18. its position at timet=0 iss(0) =11 and its velocityat timet=0 isv(0) =2. Hint: this is the same problem as thefirst. Treat acceleration as the second derivative and velocity asthe first derivative, with the distance being the original function.What is its position at timet=5?

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