Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
The practice final exam for math 1441, a college-level mathematics course focusing on limits, derivatives, differentials, and integrals. The exam includes problems on finding limits, computing derivatives, using differentials to estimate area changes, applying newton's method, determining the domains and intervals of increase/decrease/concavity, and computing definite integrals. Students are required to show their work and box their answers.
Typology: Exams
1 / 6
This page cannot be seen from the preview
Don't miss anything!
Math 1441 Practice Final Name F. Ziegler Fall 2005
Show your work to receive credit, and box your final answer in every computation.
(a) lim x→ 2
x^2 − 2 x x^2 − x − 2
(b) lim x→0+
x
x
x^2
(a) f (x) =
x^1 /^2
x^1 /^3
x^1 /^4
(b) g(x) =
x cos x
(c) h(x) = sin(x cos x)
(b) Deduce the value of a root correct to six decimal places.
(c) Is there any other root than the one you found in (b)? Cite the theorem that justifies your answer.
(d) Find the global min and max of x^5 + x − 1 for x in the interval [1, 2].
(a)
x +
x
dx
(b)
x^3
x^4 + 1 dx
(c)
x^7
x^4 + 1 dx
(a)
∫ (^) π/ 2
0
sin 2t sin t
dt
(b)
∫ (^) π/ 2
0
cos t sin(sin t) dt
(c)
∫ (^) π/ 2
0
(2 sin t − 2 sin^2 t) dt [Hint: 2 sin^2 t = 1 − cos 2t.]
2
2
! 1 ! 1
1
! 2
! 2
1
A strophoid has equation y^2 = x^2
1 − x 1 + x
(a) Use implicit differentiation to find an equation of its tangent line at the point with coordinates (x, y) = (^12 ,
√ 3 6 ).
(b) Set up the integral for the area of its loop. Then show that the substitution x = sin t reduces it to one of the integrals of problem 7. [Hint: dx =
1 − sin^2 t dt.]
