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Question Number 85540 Answers: 1 Comments: 0

find the range y=((x+[x])/(1−[x]+x))

$f i n d t h e r a n g e$ $y = \frac{x + [x]}{1 - [x] + x}$

Question Number 85535 Answers: 0 Comments: 0

Question Number 85534 Answers: 1 Comments: 2

Question Number 85532 Answers: 1 Comments: 0

Find the term independent of x in the expression of (2x−(1/(2x)))^9

$F i n d t h e t e r m i n d e p e n d e n t o f x i n t h e e x p r e s s i o n o f {(2 x - \frac{1}{2 x})}^{9}$

Question Number 85523 Answers: 1 Comments: 1

Question Number 85589 Answers: 0 Comments: 0

∫((1+4u)/(−4u^2 +2u+2))du

$\int \frac{1 + 4 u}{- {4 u}^{2} + 2 u + 2} du$

Question Number 85503 Answers: 1 Comments: 0

(dy/dx) = sec (x+y)

$\frac{d y}{d x} = \sec (x + y)$

Question Number 85500 Answers: 1 Comments: 0

The function of f and g are defined by f:g→(x/(bx−2)), x ≠ (2/b) and b ≠ 0, where a and b are real numbers g:x →2x−11 (a) If f(2)= ((-1)/2) and f^(−1) (1) = -1, find a and b and write down the expression for f in terms of x (b) Find the value of x for which fg(x)= ((-1)/2)

$T h e f u n c t i o n o f f a n d g a r e d e f i n e d b y f : g \to \frac{x}{b x - 2}, x \neq \frac{2}{b} a n d b \neq 0, w h e r e a a n d b a r e r e a l n u m b e r s g : x \to 2 x - 11$ $(a) I f f (2) = \frac{- 1}{2} a n d f^{- 1} (1) = - 1, f i n d a a n d b a n d w r i t e d o w n t h e e x p r e s s i o n f o r f i n t e r m s o f x$ $(b) F i n d t h e v a l u e o f x f o r w h i c h fg (x) = \frac{- 1}{2}$

Question Number 85498 Answers: 1 Comments: 1

(1−x^2 )(dy/(dx ))−2xy=0

$(1 - x^{2}) \frac{d y}{d x} - 2 x y = 0$

Question Number 85490 Answers: 0 Comments: 3

Given that the expression 2x^3 +px^2 −8x+9 is exactly divisable by x^2 −6x+5, find the value of p and q. Hence factorise the expression fully

$G i v e n t h a t t h e e x p r e s s i o n 2 x^{3} + {p x}^{2} - 8 x + 9 i s e x a c t l y d i v i s a b l e b y x^{2} - 6 x + 5, f i n d t h e v a l u e o f p a n d q . H e n c e f a c t o r i s e t h e e x p r e s s i o n f u l l y$

Question Number 85489 Answers: 0 Comments: 2

Find all angles between 0° and 360°, for which 8sinθ=3cos^2 θ

$F i n d a l l a n g l e s b e t w e e n 0 ° a n d 360 °, f o r w h i c h 8 s i n θ = 3 {c o s}^{2} θ$

Question Number 85488 Answers: 1 Comments: 0

∫ (dx/((x^4 +x^2 +1)^(3/4) ))

$\int \frac{d x}{{(x^{4} + x^{2} + 1)}^{\frac{3}{4}}}$

Question Number 85484 Answers: 1 Comments: 0

show that (1/(secθ+1))+(1/(secθ−1))≡2cosecθcotθ

$s h o w t h a t \frac{1}{s e c θ + 1} + \frac{1}{s e c θ - 1} \equiv 2 c o s e c θ c o t θ$

Question Number 85480 Answers: 1 Comments: 0

∫((csc(x))/(cos(x)+cos^3 (x)+...+cos^(2n+1) (x)))dx ∀x∈n

$\int \frac{c s c (x)}{c o s (x) + {c o s}^{3} (x) + . . . + {c o s}^{2 n + 1} (x)} d x$ $\forall x \in n$

Question Number 85472 Answers: 1 Comments: 4

Question Number 85513 Answers: 1 Comments: 0

Solve the following equation: ((dy/dx))^2 +2y cot x (dy/dx) = y^2

$Solve the following equation :$ ${(\frac{dy}{dx})}^{2} + 2 y \cot x \frac{dy}{dx} = y^{2}$

Question Number 85468 Answers: 1 Comments: 0

∫ln(1−e^x ) dx

$\int l n (1 - e^{x}) d x$

Question Number 85462 Answers: 0 Comments: 0

Question Number 85456 Answers: 0 Comments: 7

∫ (√(csc x )) dx?

$\int \sqrt{\csc x} dx ?$

Question Number 85447 Answers: 1 Comments: 5

Question Number 85442 Answers: 1 Comments: 1

Question Number 85441 Answers: 1 Comments: 0

∫ ((6x^4 −4)/(√(x^4 −2))) dx = ?

$\int \frac{{6 x}^{4} - 4}{\sqrt{x^{4} - 2}} dx = ?$

Question Number 85433 Answers: 1 Comments: 0

−log_(((x/6))) (((log_(10) (√(6−x)))/(log_(10) x))) > log_(10) (((∣x∣)/x))

$- \log_{(\frac{x}{6})} (\frac{\log_{10} \sqrt{6 - x}}{\log_{10} x}) > \log_{10} (\frac{∣ x ∣}{x})$

Question Number 85426 Answers: 1 Comments: 4

∫ _(π/4)^0 ((sin x+cos x)/(9+16sin 2x)) dx

$\int_{\frac{π}{4}}^{0} \frac{\sin x + \cos x}{9 + 16 \sin 2 x} d x$

Question Number 85418 Answers: 0 Comments: 1

Find the term indepent of x in the expression of (2x−(1/(2x)))^9

$F i n d t h e t e r m i n d e p e n t o f x i n t h e e x p r e s s i o n o f {(2 x - \frac{1}{2 x})}^{9}$

Question Number 85414 Answers: 1 Comments: 1

∫(1/(1+(√(cos(x))) )) dx

$\int \frac{1}{1 + \sqrt{c o s (x)}} d x$

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