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Question Number 8635 Answers: 1 Comments: 0

Find the value of x 5^(√x) − 5^x − 7 = 100

$Find the value of x$ $5^{\sqrt{x}} - 5^{x} - 7 = 100$

Question Number 8633 Answers: 1 Comments: 2

Find lim_(n→∞) (n^p /x^n ) where p∈Z^+ .

$Find \lim_{n \to \infty} \frac{n^{p}}{x^{n}} where p \in Z^{+} .$

Question Number 8632 Answers: 1 Comments: 0

evaluate ∫_0 ^3 ∫_0 ^4 1+x dy dx

$e v a l u a t e$ $\underset{0}{\int^{3}} \underset{0}{\int^{4}} 1 + x d y d x$

Question Number 8628 Answers: 1 Comments: 0

is it always satisfying? A=lim[n→∞]∫f(n,x)dx B=∫lim[n→∞]f(n,x)dx A=B?? please show counter example checking (1) f(n,x)=x^n ,x[0→1] A=lim_(n→∞) ∫_0 ^1 x^n dx=lim_(n→∞) (1/(n+1))x^(n+1) =0 B=∫_0 ^1 lim_(n→∞) x^n dx=∫_0 ^1 0dx=0 so A=B (2) f(n,x)=(1+(x/n))^n A=lim_(n→∞) ∫(1+(x/n))^n dx =lim_(n→∞) (n/((n+1)))(1+(x/n))^(n+1) =e^x B=∫lim_(n→∞) (1+(x/n))^n dx =∫e^x dx =e^x so A=B . . .

$i s i t a l w a y s s a t i s f y i n g ?$ $A = \lim [n \to \infty] \int f (n, x) d x$ $B = \int \lim [n \to \infty] f (n, x) d x$ $A = B ? ?$ $p l e a s e s h o w c o u n t e r e x a m p l e$ $c h e c k i n g$ $(1)$ $f (n, x) = x^{n}, x [0 \to 1]$ $A = {l i m}_{n \to \infty} \int_{0}^{1} x^{n} d x = {l i m}_{n \to \infty} \frac{1}{n + 1} x^{n + 1} = 0$ $B = \int_{0}^{1} {l i m}_{n \to \infty} x^{n} d x = \int_{0}^{1} 0 d x = 0$ $s o A = B$ $(2)$ $f (n, x) = {(1 + \frac{x}{n})}^{n}$ $A = {l i m}_{n \to \infty} \int {(1 + \frac{x}{n})}^{n} d x$ $= {l i m}_{n \to \infty} \frac{n}{(n + 1)} {(1 + \frac{x}{n})}^{n + 1}$ $= e^{x}$ $B = \int {l i m}_{n \to \infty} {(1 + \frac{x}{n})}^{n} d x$ $= \int e^{x} d x$ $= e^{x}$ $s o A = B$ $. . .$

Question Number 8618 Answers: 1 Comments: 1

Question Number 8609 Answers: 3 Comments: 0

Question Number 8608 Answers: 2 Comments: 0

if any angle of equilateral triangle is (− 1, 2) and any one side is x − (√(3y)) + 5 = 0 then equation of the other two sides are ??

$if any angle of equilateral triangle is$ $(- 1, 2) and any one side is x - \sqrt{3 y} + 5 = 0$ $then equation of the other two sides are ? ?$

Question Number 8607 Answers: 1 Comments: 0

Question Number 8602 Answers: 1 Comments: 0

Find the value of p and q that will make x^4 + 13x^3 + 6x^2 + px + q a perfect square

$Find the value of p and q that will make$ $x^{4} + {13 x}^{3} + {6 x}^{2} + px + q$ $a perfect square$

Question Number 8600 Answers: 1 Comments: 1

Test 1=(√1)=(√((−1)(−1)))=(√(−1))∙(√(−1)) =i∙i=i^2 =−1 so 1=−1 Find the error.

$T e s t$ $1 = \sqrt{1} = \sqrt{(- 1) (- 1)} = \sqrt{- 1} \cdot \sqrt{- 1}$ $= i \cdot i = i^{2} = - 1$ $s o 1 = - 1$ $F i n d t h e e r r o r .$

Question Number 8595 Answers: 0 Comments: 1

Let N ∈ Z. Show that Σ_(k=1) ^(N−1) ((N−k)/(sin(kπ/N))) > 2N−2+Σ_(k=2) ^(N−1) ((N−k)/(sin((k−1)π/(N−1)))) if, and only if, N ≥ 12

$L e t N \in Z . S h o w t h a t$ $\underset{k = 1}{\sum^{N - 1}} \frac{N - k}{s i n (k π / N)} > 2 N - 2 + \underset{k = 2}{\sum^{N - 1}} \frac{N - k}{s i n ((k - 1) π / (N - 1))}$ $i f, a n d o n l y i f, N ⩾ 12$

Question Number 8585 Answers: 0 Comments: 2

Question Number 8582 Answers: 1 Comments: 0

9×9

$9 \times 9$

Question Number 8578 Answers: 2 Comments: 0

Question Number 8571 Answers: 3 Comments: 2

Question Number 8564 Answers: 0 Comments: 3

Question Number 8560 Answers: 0 Comments: 1

(n/2^k )=m, n,m,k∈Z For any integer n, how many times can you divide it by 2, such that the result is always a whole number. e.g. 120 160/2=80 80/2=40 40/2=20 20/2=10 10/2=5 5/2∉Z ∴divides 5 times (n/2^k )=m ⇒ ((160)/2^k )=5 2^k =((160)/5)=32=2^5 k=5

$\frac{n}{2^{k}} = m, n, m, k \in Z$ $For any integer n, how many times$ $can you divide it by 2, such that the$ $result is always a whole number .$ $e . g . 120$ $160 / 2 = 80$ $80 / 2 = 40$ $40 / 2 = 20$ $20 / 2 = 10$ $10 / 2 = 5$ $5 / 2 \notin Z$ $∴ divides 5 times$ $\frac{n}{2^{k}} = m \Rightarrow \frac{160}{2^{k}} = 5$ $2^{k} = \frac{160}{5} = 32 = 2^{5}$ $k = 5$