{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 13 - 5 Find the general solution of the following...

This preview shows pages 1–8. Sign up to view the full content.

CALCULUS II EXAM 1 Show all your work to recive full credit. Calculators are not allowed. Closed book, closed notes. .. GOOD LUCK ! NAME : 1.) Calculate the following limits ( a ) lim x →∞ ( x 3 + 1) 1 ln( x ) , ( b ) lim x 0 ( 1 sin( x ) - 1 x ) .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2.) a.) Determine whether or not the following improper integrals converge or diverge. To receive full credit indicate what tests you are using and show all your steps. ( a 1 ) Z e 1 x (ln( x )) 2 dx, ( a 2 ) Z 1 0 e x x dx, 2
b.)Determine whether or not the following inﬁnite series converge or diverge. To receive full credit indicate what tests you are using and show all your steps ( b 1 ) X k =1 2 k + k k 3 + k , ( b 2 ) X k =1 2 k k ! k k , ( b 3 ) X k =1 ( - 1) k k + 2 k 2 + k . 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
3.) Expand g ( x ) = x ln( x ) in powers of x - 2 . 4
4.) a.) Find the interval of convergence for the power series X k =1 ( - 1) k k 2 ( k + 1)! ( x + 3) k . b.) Sum the given series X k =0 1 k ! x 3 k +1 . 5

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 5.) Find the general solution of the following diﬀerential equation xy-y = 2 x ln( x ) . 6 6.) Consider the function(transformation) from R 2 to R 2 deﬁned by f ( ± x y ² ) = ± x 2-y 2 x-2 ² . a.) Find all solutions of f ( ± x y ² ) = ± ² . b.) Is f invertible? If so, ﬁnd a formula for the inverse. If not, explain why not. 7 7.) Consider the following transformations from R 2 to R 2 . Which ones are linear? Explain your answers and for those that are linear, write down the corresponding matrix. a.) f ( ± x y ² ) = ± y + x y-x ² . b.) g ( ± x y ² ) = ± | x | y-x ² . c.) h ( ± x y ² ) = ± x 2-y 2 x 2 + y 2 ² . 8...
View Full Document

{[ snackBarMessage ]}

### Page1 / 8

13 - 5 Find the general solution of the following...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online