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Question Number 216582 Answers: 0 Comments: 3

using first principle solve y=((x+2)/( (√x)+2)) is it possible with first principle

$using first principle solve$ $y = \frac{x + 2}{\sqrt{x} + 2}$ $is it possible with first principle$

Question Number 216579 Answers: 0 Comments: 0

∫_0 ^(π/4) ∫_0 ^(π/4) ((tan(x^2 +y^2 )+sin(x^2 +y^2 ))/(tan(x^2 +y^2 )+cos(x^2 +y^2 )))dxdy

$\int_{0}^{\frac{π}{4}} \int_{0}^{\frac{π}{4}} \frac{\tan (x^{2} + y^{2}) + \sin (x^{2} + y^{2})}{\tan (x^{2} + y^{2}) + \cos (x^{2} + y^{2})} d x d y$

Question Number 216560 Answers: 1 Comments: 0

An object of mass M, initially at rest at the coordinate origin, explodes into three parts. Fragment A has a mass M/2, and fragments B and C have a mass M/4 each. After the explosion, fragment A moves in the +X direction at 10 m/s and fragment B moves in the +Y direction at 8 m/s. Find the direction and speed of fragment C

Question Number 216542 Answers: 0 Comments: 1

if y=cosu then prove that y′=sinu∙u′ by newton′s formula.

$i f y = c o s u t h e n p r o v e t h a t y^{'} = s i n u \cdot u^{'}$ $b y {n e w t o n}^{'} s f o r m u l a .$

Question Number 216538 Answers: 0 Comments: 4

Find all integer solutions of 3^m =2n^2 +1. I only found m=1, 2, 5 by computer from m=1 to m=30000. Is there any greater solutions?

$Find all integer solutions of$ $3^{m} = 2 n^{2} + 1 .$ $I o n l y f o u n d m = 1, 2, 5 b y c o m p u t e r$ $f r o m m = 1 t o m = 30000 .$ $I s t h e r e a n y g r e a t e r s o l u t i o n s ?$

Question Number 216537 Answers: 0 Comments: 0

using first principle solve y=((x+2)/( (√x)+2)) is it possible with first principle

$using first principle solve$ $y = \frac{x + 2}{\sqrt{x} + 2}$ $is it possible with first principle$

Question Number 216534 Answers: 0 Comments: 24

Question Number 216572 Answers: 1 Comments: 0

Question Number 216532 Answers: 2 Comments: 0

Let f :R_+ →R such as f(xy)=f(x)+f(y) 1) Prove that f is derivable iff f is derivable at x=1. 2) Prove that if so, f(x)=Log_a x) where a is positive value to precise

$L e t f : R_{+} \to R s u c h a s f (x y) = f (x) + f (y)$ $1) P r o v e t h a t f i s d e r i v a b l e i f f$ $f i s d e r i v a b l e a t x = 1 .$ $2) P r o v e t h a t i f s o, f (x) = {L o g}_{a} x)$ $w h e r e a i s p o s i t i v e v a l u e t o p r e c i s e$

Question Number 216526 Answers: 1 Comments: 0

Question Number 216525 Answers: 2 Comments: 0

Question Number 216515 Answers: 2 Comments: 0

Question Number 216513 Answers: 0 Comments: 0

Prove or disprove that: If p=(√(Σ_(k=0) ^n 3^k )) (n>0) is an integer, then p is prime.

$Prove or disprove that :$ $If p = \sqrt{\underset{k = 0}{\sum^{n}} 3^{k}} (n > 0) is an integer, then p is prime .$

Question Number 216507 Answers: 0 Comments: 1

Question Number 216493 Answers: 1 Comments: 0

Res_(z=c) {f(z)}=(1/(2πi)) ∮_( C) f(z)dz Res_(z=1) {((z^(21) +z^2 +z+1)/((z−1)^3 ))}=(1/(2πi)) ∮_( C) ((z^(21) +z^2 +z+1)/((z−1)^3 ))dz (1/(2πi)) ∮_( C) (((z^(21) +z^2 +z+1)/((z−1)^2 ))/(z−1))dz=lim_(z→1) ((z^(21) +z^2 +z+1)/((z−1)^2 )) L′hosiptal :) lim_(z→1) ((21z^(20) +2z+1)/(2(z−1))) and... Twice!! lim_(z→1) ((420z^(19) +2)/2)=211 ∴Res_(z=1) {f(z)}=211 ★Caution★ f(α)′′=′′(1/(2πi)) ∮_( C) ((f(z))/(z−α)) dz Why did I use big quotes for this equation?? because the conditions for establshing this equation are that path C must be a simple closed curve and there must be no singularity in path C

${Res}_{z = c} {f (z)} = \frac{1}{2 π i} \oint_{C} f (z) d z$ ${Res}_{z = 1} {\frac{z^{21} + z^{2} + z + 1}{{(z - 1)}^{3}}} = \frac{1}{2 π i} \oint_{C} \frac{z^{21} + z^{2} + z + 1}{{(z - 1)}^{3}} d z$ $\frac{1}{2 π i} \oint_{C} \frac{\frac{z^{21} + z^{2} + z + 1}{{(z - 1)}^{2}}}{z - 1} d z = \lim_{z \to 1} \frac{z^{21} + z^{2} + z + 1}{{(z - 1)}^{2}}$ $L^{'} hosiptal :)$ $\lim_{z \to 1} \frac{21 z^{20} + 2 z + 1}{2 (z - 1)} and . . . Twice!!$ $\lim_{z \to 1} \frac{420 z^{19} + 2}{2} = 211$ $∴ {Res}_{z = 1} {f (z)} = 211$ $★ Caution ★$ $f {(α)}^{″} =^{″} \frac{1}{2 π i} \oint_{C} \frac{f (z)}{z - α} d z$ $Why did I use big quotes for this$ $equation ? ?$ $because the conditions for establshing$ $this equation are that path C$ $must be a simple closed curve$ $and there must be no singularity$ $in path C$