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DifferentiationQuestion and Answers: Page 12

Question Number 162804 Answers: 2 Comments: 0

Ω = ∫ sin^( 2) (x).cos^( 4) (x ) dx

$Ω = \int {s i n}^{2} (x) . {c o s}^{4} (x) d x$

Question Number 162701 Answers: 1 Comments: 0

Question Number 162675 Answers: 1 Comments: 0

y = (√x) Find (dy/dx) by first principle.

$y = \sqrt{x}$ $F i n d \frac{d y}{d x} b y f i r s t p r i n c i p l e .$

Question Number 162516 Answers: 0 Comments: 1

differenciate using implicit function 2x+4y+sin xy=3

$d i f f e r e n c i a t e u s i n g i m p l i c i t f u n c t i o n 2 x + 4 y + \sin x y = 3$

Question Number 162424 Answers: 1 Comments: 0

calculate Ω = Σ_(n=1) ^∞ (( (−1)^( n) n)/(3^( n) (2n −1 ))) =? − Inspired from Sir Ghaderi′s post−

$c a l c u l a t e$ $Ω = \underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n} n}{3^{n} (2 n - 1)} = ?$ $- I n s p i r e d f r o m S i r G {h a d e r i}^{'} s p o s t -$

Question Number 162395 Answers: 0 Comments: 1

Question Number 162377 Answers: 1 Comments: 2

prove that ψ′′ ((1/4) )= −2π^( 3) − 56 ζ (3 )

$p r o v e t h a t$ $ψ^{″} (\frac{1}{4}) = - 2 π^{3} - 56 ζ (3)$

Question Number 162371 Answers: 2 Comments: 0

If x ∈R the maximum value of ((3x^2 +9x+17)/(3x^2 +9x+7)) is ...

$I f x \in R t h e m a x i m u m v a l u e$ $o f \frac{3 x^{2} + 9 x + 17}{3 x^{2} + 9 x + 7} i s . . .$

Question Number 162336 Answers: 1 Comments: 0

lim_( n→∞) ((1/(1+n^( 3) )) +(( 4)/(8 +n^( 3) )) + (9/(27 +n^( 3) )) +...+(n^( 2) /(2n^( 3) )) )=?

${l i m}_{n \to \infty} (\frac{1}{1 + n^{3}} + \frac{4}{8 + n^{3}} + \frac{9}{27 + n^{3}} + . . . + \frac{n^{2}}{2 n^{3}}) = ?$

Question Number 162168 Answers: 0 Comments: 0

Solve the integro−differential equation: i(t) + 4(di/dt) + ∫i(t)dt = 2 cos (3t+ 60°) where i(t) is a sinulsodial current.

$Solve the integro - differential$ $equation :$ $i (t) + 4 \frac{d i}{d t} + \int i (t) d t = 2 \cos (3 t + 60 °)$ $where i (t) is a sinulsodial current .$

Question Number 162025 Answers: 0 Comments: 0

write the taylor expansion of : f(x)= x^( 2) . cos(x) at x=1 then f^( (5 )) (x) at x=1 ?

$w r i t e t h e t a y l o r e x p a n s i o n o f :$ $f (x) = x^{2} . c o s (x) a t x = 1$ $t h e n f^{(5)} (x) a t x = 1 ?$

Question Number 162026 Answers: 2 Comments: 0

prove that.... ( 1+ (1/n) )^( n) < e < (1+(1/n) )^( n+1)

$p r o v e t h a t . . . .$ ${(1 + \frac{1}{n})}^{n} < e < {(1 + \frac{1}{n})}^{n + 1}$

Question Number 161875 Answers: 0 Comments: 0

Question Number 161802 Answers: 1 Comments: 0

Question Number 161750 Answers: 0 Comments: 2

differenciate xsin xcos x

$d i f f e r e n c i a t e x \sin x \cos x$

Question Number 161406 Answers: 0 Comments: 0

f (x ) = cos^( 2) ( x ) + sin^( 4) ( x ) R_( f) = ? −−−solution−−− y = cos^( 2) (x ) + sin^( 2) (x) .( 1−cos^( 2) (x)) = 1 − (1/4) sin^( 2) ( 2x) we know that : 0≤ sin^( 2) ( αx) ≤1 therefore −1≤− sin^( 2) (2x) ≤ 0 1−(1/4) ≤ 1− (1/4) sin^( 2) (2x) ≤1 R_( f) = [ (3/4) , 1 ] ◂ ★ ▶

$f (x) = {c o s}^{2} (x) + {s i n}^{4} (x)$ $R_{f} = ?$ $- - - s o l u t i o n - - -$ $y = {c o s}^{2} (x) + {s i n}^{2} (x) . (1 - {c o s}^{2} (x))$ $= 1 - \frac{1}{4} {s i n}^{2} (2 x)$ $w e k n o w t h a t :$ $0 ⩽ {s i n}^{2} (α x) ⩽ 1$ $t h e r e f o r e$ $- 1 ⩽ - {s i n}^{2} (2 x) ⩽ 0$ $1 - \frac{1}{4} ⩽ 1 - \frac{1}{4} {s i n}^{2} (2 x) ⩽ 1$ $R_{f} = [\frac{3}{4}, 1] ◂ ★ ▸$

Question Number 161369 Answers: 2 Comments: 0

Determine the value of the following proposition . ( True or False ) ∃ x ∈ R ; determinant ((( 1+2x),( 2x),(2x)),(( 2x),( 1+2x),( 2x )),(( 2x),( 2x),(1 +2x)))= x^( 3) + 8x−2 −−−−−−−−−

$D e t e r m i n e t h e v a l u e o f t h e f o l l o w i n g$ $p r o p o s i t i o n . (T r u e o r F a l s e)$ $\exists x \in R; | \begin{matrix} 1 + 2 x & 2 x & 2 x \\ 2 x & 1 + 2 x & 2 x \\ 2 x & 2 x & 1 + 2 x \end{matrix} | = x^{3} + 8 x - 2$ $- - - - - - - - -$

Question Number 161311 Answers: 2 Comments: 0

Differentiate y=sin xy

$D i f f e r e n t i a t e y = \sin x y$

Question Number 161209 Answers: 0 Comments: 1

Differentiate y=e^(−x^2 )

$D i f f e r e n t i a t e y = e^{- x^{2}}$

Question Number 161136 Answers: 2 Comments: 0

≺ X , τ ≻ is a topological space and A ⊆ X , A^− =^? ∩_(F⊃A) F ( F is closed set )

$≺ X, τ ≻ i s a t o p o l o g i c a l s p a c e$ $a n d A \subseteq X,$ $\bar{A} \overset{?}{=} \underset{F \supset A}{\cap} F (F i s c l o s e d s e t)$

Question Number 161130 Answers: 1 Comments: 0

Given P(x) is polynomial such that P(3x)= P ′(x).P ′′(x) . Find the tangent of curve y = P(x) parallel to the line y= 4x−2.

$G i v e n P (x) i s p o l y n o m i a l s u c h t h a t$ $P (3 x) = P^{'} (x) . P^{″} (x) . F i n d t h e t a n g e n t$ $o f c u r v e y = P (x) p a r a l l e l t o t h e l i n e$ $y = 4 x - 2 .$

Question Number 160968 Answers: 1 Comments: 0

Question Number 160967 Answers: 0 Comments: 0

Question Number 160933 Answers: 1 Comments: 0

In the given equation below , applying the formula for the derivative of inverse trigonometric functions , what is the ′′u ′′ from the given function. y = cosec^(−1) [ sin (((1+sin x)/(cos x)))]

$I n t h e g i v e n e q u a t i o n b e l o w, a p p l y i n g$ $t h e f o r m u l a f o r t h e d e r i v a t i v e o f$ $i n v e r s e t r i g o n o m e t r i c f u n c t i o n s,$ $w h a t i s t h e^{″} u^{″} f r o m t h e g i v e n f u n c t i o n .$ $y = {cosec}^{- 1} [\sin (\frac{1 + \sin x}{\cos x})]$

Question Number 160837 Answers: 0 Comments: 4

Question Number 160822 Answers: 0 Comments: 0

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