Question and Answers Forum

AllQuestion and Answers: Page 105

Question Number 206808 Answers: 2 Comments: 0

lim_(x→0) ((10^x −1)/x^(10) )

$\lim_{x \to 0} \frac{10^{x} - 1}{x^{10}}$

Question Number 206806 Answers: 0 Comments: 0

Given is a square with side length 15. We need to find exactly 17 smaller squares to fill the big one. How many solutions are possible? (Note: it′s not enough to find squares with the sum of their areas being 225, they must fit into the 15×15 square. Example with 3 squares: 2×2+5×5+14×14=225 but you cannot fit these in a 15×15 square)

$Given is a square with side length 15 .$ $We need to find exactly 17 smaller squares$ $to fill the big one . How many solutions are$ $possible ?$ $(Note : {it}^{'} s not enough to find squares with$ $the sum of their areas being 225, they must$ $fit into the 15 \times 15 square . Example with$ $3 squares : 2 \times 2 + 5 \times 5 + 14 \times 14 = 225 but$ $you cannot fit these in a 15 \times 15 square)$

Question Number 206805 Answers: 2 Comments: 0

Question Number 206804 Answers: 2 Comments: 0

Question Number 206795 Answers: 0 Comments: 3

Question Number 206794 Answers: 1 Comments: 0

help me... ∫_0 ^∞ ((sin(t)ln(t))/t)e^(−t) dt

$h e l p m e . . .$ $\int_{0}^{\infty} \frac{\sin (t) \ln (t)}{t} e^{- t} d t$

Question Number 206787 Answers: 0 Comments: 1

Question Number 206789 Answers: 1 Comments: 0

Question Number 206788 Answers: 1 Comments: 0

Question Number 206783 Answers: 1 Comments: 1

Question Number 206781 Answers: 0 Comments: 0

Question Number 206779 Answers: 2 Comments: 0

Question Number 206773 Answers: 0 Comments: 3

∫_0 ^∞ (e^(−x^2 ) /((x^2 +(1/2))^2 ))dx= I^2 =∫∫_( D) (e^(−x^2 −y^2 ) /((x^2 +(1/2))^2 (y^2 +(1/2))^2 ))dA x=rcos(θ) y=rsin(θ) J=∣((∂(x,y))/(∂(r,θ)))∣drdθ=rdrdθ ∫∫_( D) ((re^(−r^2 ) )/((r^2 cos^2 (θ)+(1/2))^2 (r^2 sin^2 (θ)+(1/2))^2 ))drdθ

$\int_{0}^{\infty} \frac{e^{- x^{2}}}{{(x^{2} + \frac{1}{2})}^{2}} d x =$ $I^{2} = \int \int_{D} \frac{e^{- x^{2} - y^{2}}}{{(x^{2} + \frac{1}{2})}^{2} {(y^{2} + \frac{1}{2})}^{2}} d A$ $x = r \cos (θ) y = r \sin (θ)$ $J =∣ \frac{\partial (x, y)}{\partial (r, θ)} ∣ d r d θ = r d r d θ$ $\int \int_{D} \frac{{r e}^{- r^{2}}}{{(r^{2} \cos^{2} (θ) + \frac{1}{2})}^{2} {(r^{2} \sin^{2} (θ) + \frac{1}{2})}^{2}} d r d θ$