One of the numbers is 40 and the other one is 63
confirmation:
63×(2/3)-2=40
and 40+63=103
Implicit differentiation:
differentiate both sides,
8e^(8x)=cos(x+4y)(1+4y')
Solve for y' to get
y'=[cos(x+4y)-8e^(8x)]/[4cos(x+4y)]
Answer:
18.8
Step-by-step explanation:
multiply pi by the diameter (6 cm) and you get the circumference
hope that helps
Answer:
Required solution gives series (a) divergent, (b) convergent, (c) divergent.
Step-by-step explanation:
(a) Given,

To applying limit comparison test, let
and
. Then,

Because of the existance of limit and the series
is divergent since
where
, given series is divergent.
(b) Given,

Again to apply limit comparison test let
and
we get,

Since
is convergent, by comparison test, given series is convergent.
(c) Given,
. Now applying Cauchy Root test on last two series, we will get,
- \lim_{n\to \infty}|(\frac{5}{6})^n|^{\frac{1}{n}}=\frac{5}{6}=L_1
- \lim_{n\to \infty}|(\frac{1}{3})^n|^{\frac{1}{n}}=\frac{1}{3}=L_2
Therefore,

Hence by Cauchy root test given series is divergent.