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Question Number 138154 Answers: 1 Comments: 0

Question Number 138153 Answers: 1 Comments: 0

lim_(x→0^+ ) ((x−∣tanx∣)/(∣sinx∣−x))=?

$\lim_{x \to 0^{+}} \frac{x - ∣ t a n x ∣}{∣ s i n x ∣ - x} = ?$

Question Number 138150 Answers: 2 Comments: 0

Given (x+(√(x^2 +1)))(y+(√(y^2 +4)))=9 find the value of x(√(y^2 +4)) + y(√(x^2 +1)) .

$G i v e n (x + \sqrt{x^{2} + 1}) (y + \sqrt{y^{2} + 4}) = 9$ $f i n d t h e v a l u e o f$ $x \sqrt{y^{2} + 4} + y \sqrt{x^{2} + 1} .$

Question Number 138145 Answers: 4 Comments: 0

...........advanced ... ... ... calculus......... find the value of:: Θ=Σ_(n=1) ^∞ (((−1)^n H_(2n) )/n)=???

$. . . . . . . . . . . a d v a n c e d . . . . . . . . . c a l c u l u s . . . . . . . . .$ $f i n d t h e v a l u e o f ::$ $Θ = \underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n} H_{2 n}}{n} = ? ? ?$

Question Number 138140 Answers: 4 Comments: 0

lim_(x→0) ((cos (sin x)−cos x)/x^4 )=?

$\lim_{x \to 0} \frac{\cos (\sin x) - \cos x}{x^{4}} = ?$

Question Number 138135 Answers: 1 Comments: 0

(x^2 +x^3 )=4 find x.

$(x^{2} + x^{3}) = 4$ $f i n d x .$

Question Number 138134 Answers: 0 Comments: 0

calculate Σ_(n=1) ^∞ (((−1)^n )/(n^3 (2n+1)^4 ))

$calculate \sum_{n = 1}^{\infty} \frac{{(- 1)}^{n}}{n^{3} {(2 n + 1)}^{4}}$

Question Number 138133 Answers: 0 Comments: 0

let A = (((1 −1)),((2 3)) ) 1)calculate e^A and e^(tA) 2)find cosA ,sinA 3) find log(1+A)

$let A = (\begin{matrix} 1 - 1 \\ 2 3 \end{matrix})$ $1) calculate e^{A} and e^{tA}$ $2) find cosA, sinA$ $3) find \log (1 + A)$

Question Number 138132 Answers: 1 Comments: 0

calculate ∫_0 ^∞ ((logx)/(x^2 −x+2))dx

$calculate \int_{0}^{\infty} \frac{logx}{x^{2} - x + 2} dx$

Question Number 138131 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/((2x+1)(x^2 −x+3)^2 ))

$calculate \int_{0}^{\infty} \frac{dx}{(2 x + 1) {(x^{2} - x + 3)}^{2}}$

Question Number 138129 Answers: 0 Comments: 0

calculate ∫_0 ^1 ((ln(2+x^2 ))/(x^2 +3))dx

$calculate \int_{0}^{1} \frac{\ln (2 + x^{2})}{x^{2} + 3} dx$

Question Number 138128 Answers: 1 Comments: 0

calculate ∫ (dx/( (√(2−x^2 ))+(√(3+x^2 ))))

$calculate \int \frac{dx}{\sqrt{2 - x^{2}} + \sqrt{3 + x^{2}}}$

Question Number 138123 Answers: 1 Comments: 0

Question Number 138120 Answers: 2 Comments: 1

Question Number 138114 Answers: 1 Comments: 2

...... calculus.....(III)...... evaluate:: 𝛗=^(???) ∫_0 ^( (π/2)) ∫_0 ^( x) ((cos(y))/( (√(((π/2)−x)((π/2)−y)))))dydx

$. . . . . . c a l c u l u s . . . . . (I I I) . . . . . .$ $e v a l u a t e ::$ $ϕ \overset{? ? ?}{=} \int_{0}^{\frac{π}{2}} \int_{0}^{x} \frac{c o s (y)}{\sqrt{(\frac{π}{2} - x) (\frac{π}{2} - y)}} d y d x$

Question Number 138112 Answers: 2 Comments: 0

prove that ∫_0 ^( (π/2)) (sin^(2k) (x)dx)=(((2k)!2^(−2k−1) )/((k!)^2 ))

$p r o v e t h a t$ $\int_{0}^{\frac{π}{2}} ({s i n}^{2 k} (x) d x) = \frac{(2 k)! 2^{- 2 k - 1}}{{(k!)}^{2}}$

Question Number 138099 Answers: 0 Comments: 5

If sin^4 α+cos^4 β = 4sin α cos β , 0≤α,β ≤ (π/2) , then sin α+cos β equal to …

$I f \sin^{4} α + \cos^{4} β = 4 \sin α \cos β,$ $0 ⩽ α, β ⩽ \frac{π}{2}, t h e n \sin α + \cos β$ $e q u a l t o \dots$

Question Number 138096 Answers: 1 Comments: 1

solve 2^x +4^x =8^x

$s o l v e$ $2^{x} + 4^{x} = 8^{x}$

Question Number 138091 Answers: 2 Comments: 0

If 3^((log _3 7)^x ) = 7^((log _7 3)^x ) , then the value of x will be …

$I f 3^{{(\log_{3} 7)}^{x}} = 7^{{(\log_{7} 3)}^{x}}, t h e n t h e$ $v a l u e o f x w i l l b e \dots$

Question Number 138089 Answers: 1 Comments: 1

Question Number 138085 Answers: 1 Comments: 0

Given a curve y = (1/(x^2 +1)). Find the equation of tangent line with have slope of tangent minimum .

$G i v e n a c u r v e y = \frac{1}{x^{2} + 1} .$ $F i n d t h e e q u a t i o n o f t a n g e n t$ $l i n e w i t h h a v e s l o p e o f t a n g e n t$ $m i n i m u m .$

Question Number 138086 Answers: 0 Comments: 0

∫_0 ^(π/2) ln(((ln^2 (sinθ))/(π^2 +ln^2 (sinθ)))) ((ln(cosθ))/(tanθ))dθ

$\int_{0}^{\frac{π}{2}} \ln (\frac{\ln^{2} (\sin θ)}{π^{2} + \ln^{2} (\sin θ)}) \frac{\ln (\cos θ)}{\tan θ} d θ$

Question Number 138077 Answers: 2 Comments: 0

∫_( 0) ^( (π/2)) (((cotx))^(1/3) +(1/( ((cotx))^(1/3) )))^2 dx

$\int_{0}^{\frac{π}{2}} {(\sqrt[3]{c o t x} + \frac{1}{\sqrt[3]{c o t x}})}^{2} d x$

Question Number 138075 Answers: 0 Comments: 0

Use the inner product ⟨f,g⟩=∫10f(x)g(x)dx in the vector space C0[0,1] of continuous functions on the domain [0,1] to find the orthogonal projection of f(x)=3x2−2 onto the subspace V spanned by g(x)=x and h(x)=1. (Caution: x and 1 do not form an orthogonal basis of V.) projV(f)= .

Use the inner product ⟨f,g⟩=∫10f(x)g(x)dx in the vector space C0[0,1] of continuous functions on the domain [0,1] to find the orthogonal projection of f(x)=3x2−2 onto the subspace V spanned by g(x)=x and h(x)=1. (Caution: x and 1 do not form an orthogonal basis of V.) projV(f)= .

Question Number 138074 Answers: 0 Comments: 0

Let W be the set of all vectors ⎡⎣⎢xyx+y⎤⎦⎥ with x and y real. Find a basis of W⊥. { ⎡⎣⎢⎢⎢⎢⎢⎢⎤⎦⎥⎥⎥⎥⎥⎥ }

Let W be the set of all vectors ⎡⎣⎢xyx+y⎤⎦⎥ with x and y real. Find a basis of W⊥. { ⎡⎣⎢⎢⎢⎢⎢⎢⎤⎦⎥⎥⎥⎥⎥⎥ }

Question Number 138073 Answers: 0 Comments: 0

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