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Question Number 66356 Answers: 1 Comments: 0

Question Number 66293 Answers: 0 Comments: 3

What do we mean by ∫_(−∞) ^(+∞) f(x) dx?

$W h a t d o w e m e a n b y$ $\int_{- \infty}^{+ \infty} f (x) d x ?$

Question Number 66285 Answers: 2 Comments: 0

What is the difference between lim_(x→2^− ) and lim_(x→2^+ )

$W h a t i s t h e d i f f e r e n c e b e t w e e n$ $\underset{x \to 2^{-}}{l i m} a n d$ $\underset{x \to 2^{+}}{l i m}$

Question Number 66228 Answers: 0 Comments: 3

prove that ∫_2 ^4 ((6x +1)/((2x−3)(3x−2)))dx = ln 10

$p r o v e t h a t$ $\int_{2}^{4} \frac{6 x + 1}{(2 x - 3) (3 x - 2)} d x = l n 10$

Question Number 66227 Answers: 0 Comments: 0

Using a good counter procedure, prove that (∂y/∂x) = lim_(∂x→0) ((f(∂ + x) −f(x))/∂x) for a given function f(x) in x.

$U s i n g a g o o d c o u n t e r p r o c e d u r e, p r o v e t h a t$ $\frac{\partial y}{\partial x} = \underset{\partial x \to 0}{l i m} \frac{f (\partial + x) - f (x)}{\partial x}$ $f o r a g i v e n f u n c t i o n f (x) i n x .$

Question Number 66226 Answers: 0 Comments: 1

the equation f(x)=0 has real roots in the interval (a, b) if A −f(a)>0 and f(b) >0 B f(a) <0 and f(b) <0 C −f(a) >0 and f(b) =0 D f(a) >0 and f(b) < 0

$t h e e q u a t i o n f (x) = 0 h a s r e a l r o o t s i n$ $t h e i n t e r v a l (a, b) i f$ $A - f (a) > 0 a n d f (b) > 0$ $B f (a) < 0 a n d f (b) < 0$ $C - f (a) > 0 a n d f (b) = 0$ $D f (a) > 0 a n d f (b) < 0$

Question Number 66225 Answers: 1 Comments: 2

Given that f(x)= { ((−x + 1, x≤ 3_ )),((kx −8, x >3)) :} is continuous then f(5) = A 2 B 0 C −2 D −1

$G i v e n t h a t f (x) = {\begin{cases} - x + 1, x ⩽ 3_{} \\ k x - 8, x > 3 \end{cases}$ $i s c o n t i n u o u s t h e n f (5) =$ $A 2$ $B 0$ $C - 2$ $D - 1$

Question Number 66216 Answers: 1 Comments: 2

∣a ∣ = 3 ,∣b∣= 5 , a.b =−14 ∣a − b∣ = ?

$∣ a ∣ = 3, ∣ b ∣= 5, a . b = - 14$ $∣ a - b ∣ = ?$

Question Number 66815 Answers: 2 Comments: 1

solve the congruence equation 6x ≡ 4 (mod 5) i need help please with some explanations

$s o l v e t h e c o n g r u e n c e e q u a t i o n$ $6 x \equiv 4 (m o d 5) i n e e d h e l p p l e a s e w i t h s o m e e x p l a n a t i o n s$

Question Number 66160 Answers: 0 Comments: 0

Question Number 66149 Answers: 2 Comments: 0

f(x) =2x^3 −x−4 show that f(x) =0 has roots between 1 and 2

$f (x) = 2 x^{3} - x - 4$ $s h o w t h a t f (x) = 0 h a s r o o t s b e t w e e n$ $1 a n d 2$

Question Number 66140 Answers: 0 Comments: 0

1.Show that: ∫_0 ^(π/2) f(sin 2x)sin x dx=(√2) ∫_0 ^(π/4) f(cos 2x)cos x dx. 2.If f(z)=(d/dz){5^(∣f(z)∣) } then what is the value of f′(e)?

$1 . S h o w t h a t : \int_{0}^{\frac{π}{2}} f (\sin 2 x) \sin x d x = \sqrt{2} \int_{0}^{\frac{π}{4}} f (\cos 2 x) \cos x d x .$ $2 . I f f (z) = \frac{d}{d z} {5^{∣ f (z) ∣}} t h e n w h a t i s t h e v a l u e o f f^{'} (e) ?$

Question Number 66116 Answers: 0 Comments: 5

Given that f(x) = { ((x, for 0≤x<2)),((0, for 2≤x≤3)) :} is periodic with period 3 units, find the value of f(5) and f(−5) sketch the graph of f(x) for x between −3 and 6 please i really need explanations when solving the first part of the question thanks

$G i v e n t h a t f (x) = {\begin{cases} x, f o r 0 ⩽ x < 2 \\ 0, f o r 2 ⩽ x ⩽ 3 \end{cases}$ $i s p e r i o d i c w i t h p e r i o d 3 u n i t s,$ $f i n d t h e v a l u e o f f (5) a n d f (- 5)$ $s k e t c h t h e g r a p h o f f (x) f o r x b e t w e e n - 3 a n d 6$ $p l e a s e i r e a l l y n e e d e x p l a n a t i o n s w h e n s o l v i n g t h e f i r s t p a r t o f t h e q u e s t i o n$ $t h a n k s$

Question Number 66115 Answers: 0 Comments: 4

find ∣z∣ where z = (((1+i(√3) )^3 )/((1−i)^3 )) find the maximum value of 12sinx − 5cosx

$f i n d ∣ z ∣ w h e r e z = \frac{{(1 + i \sqrt{3})}^{3}}{{(1 - i)}^{3}}$ $f i n d t h e m a x i m u m v a l u e o f 12 s i n x - 5 c o s x$

Question Number 66114 Answers: 1 Comments: 0

∫(((e^(2x) −sin2x)/(e^(2x) +cos2x)))dx = ?

$\int (\frac{e^{2 x} - s i n 2 x}{e^{2 x} + c o s 2 x}) d x = ?$

Question Number 66108 Answers: 0 Comments: 4

Given that the binomial expansion of ((2 + kx)/((2−5x)^(2 ) )) , ∣x∣ < (2/(5 )) ,in ascending powers of x is (1/2) + (7/4)x + Ax^2 + ..., find the values of A and k

$G i v e n t h a t t h e b i n o m i a l e x p a n s i o n o f \frac{2 + k x}{{(2 - 5 x)}^{2}}, ∣ x ∣ < \frac{2}{5}, i n a s c e n d i n g$ $p o w e r s o f x i s \frac{1}{2} + \frac{7}{4} x + {A x}^{2} + . . ., f i n d t h e v a l u e s o f A a n d k$

Question Number 66107 Answers: 0 Comments: 3

Given that S_n = ((a(1 −r^n ))/(1−r)) , r ≠ 1, show that ((S_(3n) −S_(2n) )/(S_n )) = r^(2n) hence given that r =(1/2) find Σ_(n=0) ^∞ (((S_(3n) −S_(2n) )/S_n ))

$G i v e n t h a t S_{n} = \frac{a (1 - r^{n})}{1 - r}, r \neq 1, s h o w t h a t \frac{S_{3 n} - S_{2 n}}{S_{n}} = r^{2 n}$ $h e n c e g i v e n t h a t r = \frac{1}{2} f i n d \underset{n = 0}{\sum^{\infty}} (\frac{S_{3 n} - S_{2 n}}{S_{n}})$

Question Number 66105 Answers: 0 Comments: 3

Find ∫_(−1) ^1 ((9 +4x^2 )/(9−4x^2 )) dx

$F i n d \int_{- 1}^{1} \frac{9 + 4 x^{2}}{9 - 4 x^{2}} d x$

Question Number 66104 Answers: 0 Comments: 1

f(x)= 2x^3 −x−4 show that the equation f(x) =0 has root between 1 and 2 show that the equation f(x) =0 can be written as x = (√(((2/x) +(1/2)))) use the iteration x_(n+1 ) = (√(((2/x_n ) +(1/2)) ,)) with x_0 = 1.385 to find to 3 decimal places the value of x_1 .

$f (x) = 2 x^{3} - x - 4$ $s h o w t h a t t h e e q u a t i o n f (x) = 0 h a s r o o t b e t w e e n 1 a n d 2$ $s h o w t h a t t h e e q u a t i o n f (x) = 0 c a n b e w r i t t e n a s$ $x = \sqrt{(\frac{2}{x} + \frac{1}{2})}$ $u s e t h e i t e r a t i o n$ $x_{n + 1} = \sqrt{(\frac{2}{x_{n}} + \frac{1}{2}),}$ $w i t h x_{0} = 1.385 t o f i n d t o 3 d e c i m a l p l a c e s t h e v a l u e o f x_{1} .$

Question Number 66103 Answers: 0 Comments: 2

A binary relation R is defined on N,the set of natural numbers by _x R_y ⇔ ∃ n ∈ Z : x = 2^n y, x,y ∈ N show that R is an equivalence relation

$A b i n a r y r e l a t i o n R i s d e f i n e d o n N, t h e s e t o f n a t u r a l n u m b e r s b y$ $_{x} R_{y} \Leftrightarrow \exists n \in Z : x = 2^{n} y, x, y \in N$ $s h o w t h a t R i s a n e q u i v a l e n c e r e l a t i o n$

Question Number 66102 Answers: 0 Comments: 3

prove by mathematical induction that 4^n +3^n +2 is a multiple of 3 for all positive integral values of n.

$p r o v e b y m a t h e m a t i c a l i n d u c t i o n t h a t 4^{n} + 3^{n} + 2 i s a m u l t i p l e o f 3 f o r a l l$ $p o s i t i v e i n t e g r a l v a l u e s o f n .$

Question Number 66101 Answers: 1 Comments: 1

find (dy/dx) when y = x^2 ln(3x) Given that xsinx − y^2 =0 show that y^2 = 2cosx −2((dy/dx))^2 −2y(d^2 y/dx^2 )

$f i n d \frac{d y}{d x} w h e n y = x^{2} l n (3 x)$ $G i v e n t h a t x s i n x - y^{2} = 0 s h o w t h a t y^{2} = 2 c o s x - 2 {(\frac{d y}{d x})}^{2} - 2 y \frac{d^{2} y}{{d x}^{2}}$

Question Number 66071 Answers: 1 Comments: 0

Evaluate the integral as a limit of sums: 1.∫_1 ^3 (e^(2−3x) +x^2 +1)dx

$Evaluate the integral as a limit of sums :$ $1 . \int_{1}^{3} (e^{2 - 3 x} + x^{2} + 1) d x$

Question Number 66061 Answers: 0 Comments: 0

let f(t) =∫_0 ^1 ((sinx)/(1+te^(−x^2 ) ))dx with ∣t∣<1 developp f at integr serie .

$l e t f (t) = \int_{0}^{1} \frac{s i n x}{1 + {t e}^{- x^{2}}} d x w i t h ∣ t ∣< 1$ $d e v e l o p p f a t i n t e g r s e r i e .$

Question Number 66058 Answers: 2 Comments: 5

If x + (1/x)=1 find out value:− ((x^(20) +x^(17) +x^(14) +x^(11) )/(x^(17) +x^(14) +x^(11) +x^8 )) = ?

$I f x + \frac{1}{x} = 1$ $f i n d o u t v a l u e : -$ $\frac{x^{20} + x^{17} + x^{14} + x^{11}}{x^{17} + x^{14} + x^{11} + x^{8}} = ?$

Question Number 66019 Answers: 2 Comments: 1

lim_(x→∞) (1 + (2/x))^x =

$\underset{x \to \infty}{l i m} {(1 + \frac{2}{x})}^{x} =$

Pg 80 Pg 81 Pg 82 Pg 83 Pg 84 Pg 85 Pg 86 Pg 87 Pg 88 Pg 89

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