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Unformatted text preview: Math 116 - Lab 7 - Fall 2011.
L’Hˆpital’s rule, Integration, Deﬁnite Integrals (Sections 4.5, 5.1 and 5.2 of L/G).
You are to provide full solutions to the following problems. You are allowed to collaborate with your
classmates, use your notes and textbook and ask the TA for guidance. Direct copying of solutions
is not encouraged, nor is it allowed or ethical. First name: Last name:
Student number: 1 Math 116 - Lab 7 - Fall 2011. Student number: L’Hˆpital’s rule, Integration, Deﬁnite Integrals (Sections 4.5, 5.1 and 5.2 of L/G).
o 1. Determine the value of the limit
limx→6 8x+1 , a) limx→1
b) c) limt→0+ 1 + 3
5t 8t , d) limφ→0+ (cos(3φ))cot(2φ) .
2. Use the summation formulas from p. 329 in Lutzer & Goodwill to calculate the sum.
k=1 3 ,
k=1 (12k − 7) ,
k=1 (2 − 8k − 11k ) . 3. Let y (t) = 4t + 3. Approximate the net change in y (t) over the interval [1, 6] using a
right-sampled Riemann sum with 10 subintervals.
4. Let y (t) = 9 − t2 . Approximate the net change in y (t) over the interval [1, 3] using a
right-sampled Riemann sum with 5 subintervals.
5. Write the limit using integral notation:
lim 6. Consider the integral 2 . π cos(2 + 3t)dt.
0 a) Write it as the limit of left-sampled Riemann sums.
b) Write it as the limit of right-sampled Riemann sums.
7. Calculate the area between the graphs of f (t) = 2 + t2 and g (t) = 2t over [0, 2] as the
limit of Riemann sums.
8. Write an integral for the area between the graph of sin x and the x-axis over [0, π ].
(You don’t need to evaluate the integral). 2 ...
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