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Question Number 60240 Answers: 0 Comments: 1

∫_0 ^2 ((ln(x))/(√(4−x^2 )))dx

$\underset{0}{\int^{2}} \frac{\ln (x)}{\sqrt{4 - x^{2}}} dx$

Question Number 60238 Answers: 0 Comments: 0

Question Number 60212 Answers: 1 Comments: 1

Question Number 60203 Answers: 2 Comments: 1

demonstrate ∣sin(y)−sin(x)∣≤∣y−x∣

$d e m o n s t r a t e$ $∣ s i n (y) - s i n (x) ∣⩽∣ y - x ∣$

Question Number 60202 Answers: 0 Comments: 0

construct the point M^′ =(1/2)((((z+∣z∣))/2))

$c o n s t r u c t t h e p o i n t M^{^{'}} = \frac{1}{2} (\frac{(z + ∣ z ∣)}{2})$

Question Number 60197 Answers: 1 Comments: 1

valculste lim_(n→+∞) (ln((Π_(k=1) ^n (1+(k^3 /n^3 )))^(1/n) )

$v a l c u l s t e {l i m}_{n \to + \infty} (l n ({(\prod_{k = 1}^{n} (1 + \frac{k^{3}}{n^{3}}))}^{\frac{1}{n}})$

Question Number 60198 Answers: 1 Comments: 0

find lim_(n→+∞) ln(Π_(k=1) ^n (1+(k^4 /n^4 ))^(1/n) )

$f i n d {l i m}_{n \to + \infty} l n (\prod_{k = 1}^{n} {(1 + \frac{k^{4}}{n^{4}})}^{\frac{1}{n}})$

Question Number 60189 Answers: 0 Comments: 0

Question Number 60175 Answers: 0 Comments: 2

solving u^v =w with u, v, w ∈C finding all possible solutions I tested this with several values and found no mistake. please review and comment. I hope this will help at least some of you.

$solving u^{v} = w with u, v, w \in C$ $finding all possible solutions$ $I tested this with several values and found$ $no mistake . please review and comment .$ $I hope this will help at least some of you .$

Question Number 60170 Answers: 0 Comments: 0

∫xsec^3 xdx

$\int x \sec^{3} x d x$

Question Number 60156 Answers: 3 Comments: 2

Prove by principle of mathematical induction sin(x) + sin(2x) + sin(3x) + ... + sin(nx) = ((cos((1/2)x) − cos(n + (1/2))x)/(2 sin((1/2)x)))

$Prove by principle of mathematical induction$ $\sin (x) + \sin (2 x) + \sin (3 x) + . . . + \sin (nx) = \frac{\cos (\frac{1}{2} x) - \cos (n + \frac{1}{2}) x}{2 \sin (\frac{1}{2} x)}$

Question Number 60152 Answers: 0 Comments: 16

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Question Number 60155 Answers: 1 Comments: 0

Show that: (1/2) + cos(x) + cos(2x) + ... + cos(nx) = ((sin(n + (1/2))x)/(2 sin((1/2))x)) By principle of mathematical induction

$Show that :$ $\frac{1}{2} + \cos (x) + \cos (2 x) + . . . + \cos (nx) = \frac{\sin (n + \frac{1}{2}) x}{2 \sin (\frac{1}{2}) x}$ $By principle of mathematical induction$

Question Number 60143 Answers: 1 Comments: 0

Two passenger trains, A and B, 450km apart, start to move towards each other at the same time and meet after 2 hours. If train B, travels (8/7) as fast as train A, find the speed of each train.

$Two passenger trains, A and B, 450 km apart,$ $start to move towards each other at the$ $same time and meet after 2 hours . If train B,$ $travels \frac{8}{7} as fast as train A, find the speed$ $of each train .$