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AllQuestion and Answers: Page 579

Question Number 155883 Answers: 0 Comments: 1

∫ ((tan^2 x)/(1−tan^2 x)) dx=?

$\int \frac{\tan^{2} x}{1 - \tan^{2} x} d x = ?$

Question Number 155878 Answers: 2 Comments: 0

the equation of : (a +sin(x))(a+cos(x))=a has solution in R hence : a ∈ ?

$t h e e q u a t i o n o f :$ $(a + s i n (x)) (a + c o s (x)) = a$ $h a s s o l u t i o n i n R$ $h e n c e :$ $a \in ?$

Question Number 155866 Answers: 1 Comments: 0

Question Number 155863 Answers: 0 Comments: 2

monster integral ∫_0 ^( (π/4)) ln^2 (sin(2x)+ cos(3x)) dx

$\underset{―}{monster integral}$ $\int_{0}^{\frac{π}{4}} \ln^{2} (\sin (2 x) + \cos (3 x)) d x$

Question Number 155857 Answers: 1 Comments: 0

1). Find (dy/dx) , if : a). y=(8x−1)(x^2 +4x+7) b). y=(3x^4 −10x+8)(2x^2 +5) 2). Find an equation of the tangen line to the graph of y=(5/(1+x^2 )) at each point a). P(0,5) b). Q(1,(5/2)) 3). Find the coordinat of all point on the graph of : y=x^3 +2x^2 −4x+5 at which the tangen line is: a). horizontal. b). paralel to the line y=2y+8x−5=0 4). Find point P on the graph of y=x^3 such that the tangen line at P has x−intercept 4 5). Find the points at which the graph f(x) and f^′ (x) is intersect , given that a). f(x)=x^3 −x^2 +x+1 b). f(x)=x^2 +2x+1

$1) . Find \frac{dy}{dx}, if :$ $a) . y = (8 x - 1) (x^{2} + 4 x + 7)$ $b) . y = ({3 x}^{4} - 10 x + 8) ({2 x}^{2} + 5)$ $2) . Find an equation of the tangen line$ $to the graph of y = \frac{5}{1 + x^{2}} at each point$ $a) . P (0, 5) b) . Q (1, \frac{5}{2})$ $3) . Find the coordinat of all point on$ $the graph of : y = x^{3} + {2 x}^{2} - 4 x + 5 at which the$ $tangen line is :$ $a) . horizontal .$ $b) . paralel to the line$ $y = 2 y + 8 x - 5 = 0$ $4) . Find point P on the graph of y = x^{3}$ $such that the tangen line at P has$ $x - intercept 4$ $5) . Find the points at which the graph$ $f (x) and f^{^{'}} (x) is intersect, given that$ $a) . f (x) = x^{3} - x^{2} + x + 1$ $b) . f (x) = x^{2} + 2 x + 1$

Question Number 155856 Answers: 2 Comments: 0

How many natural number from 1 to 900 which are not divisible 2,3 and 5

$How many natural number from$ $1 to 900 which are not divisible$ $2, 3 and 5$

Question Number 155849 Answers: 0 Comments: 0

Ω=∫_0 ^( ∞) log(sinh(x)).log(tanh(x))dx=((7ζ(3))/8) +(π^( 2) /8)ln^ (2)

$Ω = \int_{0}^{\infty} l o g (s i n h (x)) . l o g (t a n h (x)) d x = \frac{7 ζ (3)}{8} + \frac{π^{2}}{8} {l n}^{} (2)$

Question Number 155898 Answers: 2 Comments: 0

Show that tan^(− 1) ((1/3)) + sin^(− 1) ((1/3)) = (π/4)

$Show that \tan^{- 1} (\frac{1}{3}) + \sin^{- 1} (\frac{1}{3}) = \frac{π}{4}$

Question Number 155899 Answers: 1 Comments: 0

Find the nth root of 1. Find these values when n = 6.

$Find the nth root of 1 . Find these values when n = 6 .$

Question Number 155842 Answers: 1 Comments: 1

Prof that: Σ_(n=1) ^(10) n.n!=11!−1

$Prof that :$ $\underset{n = 1}{\sum^{10}} n . n! = 11! - 1$

Question Number 155979 Answers: 0 Comments: 0

prove that: ∫_0 ^( 1) ∫_0 ^( 1) (((√x) +(√y))/((1−xy)((xy))^(1/4) )) dxdy=4 (4 −π)

$p r o v e t h a t :$ $\int_{0}^{1} \int_{0}^{1} \frac{\sqrt{x} + \sqrt{y}}{(1 - x y) \sqrt[4]{x y}} d x d y = 4 (4 - π)$

Question Number 155978 Answers: 0 Comments: 2

Question Number 155829 Answers: 1 Comments: 2

Find this excercise about limits trigonometri 1). lim_(θ→0) ((2cos θ−2)/(3θ)) 2). lim_(x→0) ((1−cos x)/x^(2/3) ) 3). lim_(t→0) ((4t^2 +3t sin t)/t^2 ) 4). lim_(x→0) ((x^2 +1)/(x+cos x)) 5). lim_(x→0) ((sin^2 ((x/2)))/(sin x))

$Find this excercise about limits$ $trigonometri$ $1) . \lim_{θ \to 0} \frac{2 \cos θ - 2}{3 θ}$ $2) . \lim_{x \to 0} \frac{1 - \cos x}{x^{\frac{2}{3}}}$ $3) . \lim_{t \to 0} \frac{{4 t}^{2} + 3 t \sin t}{t^{2}}$ $4) . \lim_{x \to 0} \frac{x^{2} + 1}{x + \cos x}$ $5) . \lim_{x \to 0} \frac{\sin^{2} (\frac{x}{2})}{\sin x}$

Question Number 156776 Answers: 1 Comments: 1

Σ_(n=1) ^∞ (n ln(((2n+1)/(2n−1))) −1)=?

$\underset{n = 1}{\sum^{\infty}} (n l n (\frac{2 n + 1}{2 n - 1}) - 1) = ?$

Question Number 156775 Answers: 1 Comments: 1

f is a function that assigns to each natural number multiplication of its digits for exampl : f( 200)=0 f ( 128 )=1×2×8 =16 find the value of : f (100) + f(101 )+ f (102 )+...f(999)=?

$f i s a f u n c t i o n t h a t a s s i g n s$ $t o e a c h n a t u r a l n u m b e r$ $m u l t i p l i c a t i o n o f i t s d i g i t s$ $f o r e x a m p l : f (200) = 0$ $f (128) = 1 \times 2 \times 8 = 16$ $f i n d t h e v a l u e o f :$ $f (100) + f (101) + f (102) + . . . f (999) = ?$

Question Number 155816 Answers: 1 Comments: 0

How many of the number formed by using all the digits 1,2,3,4,5,6 only once divisible by 25.

$How many of the number formed$ $by using all the digits 1, 2, 3, 4, 5, 6$ $only once divisible by 25 .$

Question Number 155812 Answers: 2 Comments: 0

Use algebraic simplifications to help find the limits, if they exist. 1). lim_(x→2) ((x^2 −4)/(x−2)) 2). lim_(x→1) ((x^2 −x)/(2x^2 +5x−7)) 3). lim_(x→1) ((3x^2 −13x−10)/(2x^2 −7x−15)) 4). lim_(x→1) ((3x^2 −13x−10)/(2x^2 −7x−15)) 5). lim_(x→2) ((x^3 −8)/(x^2 −4))

$Use algebraic simplifications to help$ $find the limits, if they exist .$ $1) . \lim_{x \to 2} \frac{x^{2} - 4}{x - 2}$ $2) . \lim_{x \to 1} \frac{x^{2} - x}{{2 x}^{2} + 5 x - 7}$ $3) . \lim_{x \to 1} \frac{{3 x}^{2} - 13 x - 10}{{2 x}^{2} - 7 x - 15}$ $4) . \lim_{x \to 1} \frac{{3 x}^{2} - 13 x - 10}{{2 x}^{2} - 7 x - 15}$ $5) . \lim_{x \to 2} \frac{x^{3} - 8}{x^{2} - 4}$

Question Number 156188 Answers: 0 Comments: 2

Given a rational function f(x) = ((ax^2 +bx+c)/(x+q)) has minimum point at (−2,9) and maximum point at (2,1) . Find value of a, b, c, and q .

$G i v e n a r a t i o n a l f u n c t i o n$ $f (x) = \frac{{a x}^{2} + b x + c}{x + q}$ $h a s m i n i m u m p o i n t a t (- 2, 9) a n d m a x i m u m p o i n t a t (2, 1) .$ $F i n d v a l u e o f a, b, c, a n d q .$

Question Number 156186 Answers: 1 Comments: 2

Question Number 156184 Answers: 2 Comments: 1

Question Number 155810 Answers: 1 Comments: 0

Verify the identity in Excercise below 1). cos θsec θ=1 2). (1+cos β)(1−cos β)=sin^2 β 3). cos^2 x(sec^2 x−1)=sin^2 x 4). ((sin t)/(cosec t))+((cos t)/(sec t))=1 5). ((cosec^2 θ)/(1+tan^2 θ)) = cot^2 θ

$Verify the identity in Excercise below$ $1) . \cos θ \sec θ = 1$ $2) . (1 + \cos β) (1 - \cos β) = \sin^{2} β$ $3) . \cos^{2} x (\sec^{2} x - 1) = \sin^{2} x$ $4) . \frac{\sin t}{cosec t} + \frac{\cos t}{\sec t} = 1$ $5) . \frac{cosec^{2} θ}{1 + \tan^{2} θ} = \cot^{2} θ$

Question Number 155809 Answers: 1 Comments: 0

Given that f○g = (x^2 /(2x^2 − x + 4)) and g(x) = (x/(x − 2)), find f(x) ?

$Given that f \circ g = \frac{x^{2}}{2 x^{2} - x + 4} and$ $g (x) = \frac{x}{x - 2}, find f (x) ?$

Question Number 155806 Answers: 1 Comments: 0

Question Number 155803 Answers: 2 Comments: 0

proof that Σ_(n=1) ^(10) n×n! = 11!−1

$proof that$ $\underset{n = 1}{\sum^{10}} n \times n! = 11! - 1$

Question Number 155802 Answers: 1 Comments: 0

find the value of 2×1!+4×2!+6×3!+...+200×100!

$find the value of$ $2 \times 1! + 4 \times 2! + 6 \times 3! + . . . + 200 \times 100!$

Question Number 155801 Answers: 3 Comments: 0

{ ((m^2 =n+2)),((n^2 =m+2)) :} ⇒m≠n 4mn−m^3 −n^3 =?

${\begin{cases} m^{2} = n + 2 \\ n^{2} = m + 2 \end{cases} \Rightarrow m \neq n$ $4 mn - m^{3} - n^{3} = ?$

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