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Question Number 73572 Answers: 0 Comments: 1

determine wether or not the function f,where f(x) = { ((2x + 1, 0≤ x <2)),((7−x, 2 ≤ x < 4)),((((3x)/4) , 4 ≤ x < 6)) :} is continuous in the interval [0,6[

$d e t e r m i n e w e t h e r o r n o t t h e f u n c t i o n f, w h e r e$ $f (x) = {\begin{cases} 2 x + 1, 0 ⩽ x < 2 \\ 7 - x, 2 ⩽ x < 4 \\ \frac{3 x}{4}, 4 ⩽ x < 6 \end{cases}$ $i s c o n t i n u o u s i n t h e i n t e r v a l [0, 6 [$

Question Number 73570 Answers: 0 Comments: 1

f : x → { ((1 + x, if x<1)),((2x−1,if x>1)) :} investigate the existence and non existence of the limit of f at the point x =1

$f : x \to {\begin{cases} 1 + x, i f x < 1 \\ 2 x - 1, i f x > 1 \end{cases}$ $i n v e s t i g a t e t h e e x i s t e n c e a n d n o n e x i s t e n c e o f t h e$ $l i m i t o f f a t t h e p o i n t x = 1$

Question Number 73569 Answers: 0 Comments: 2

let f(x) = ((tanx)/(tan2x)) . Find the points of discontinuity of f on [0,2π] and determine wether each duscontinuity is a point discontinuity,a jump discontinuity,or a vertical asymtote

$l e t f (x) = \frac{t a n x}{t a n 2 x} . F i n d t h e p o i n t s o f d i s c o n t i n u i t y$ $o f f o n [0, 2 π] a n d d e t e r m i n e w e t h e r e a c h d u s c o n t i n u i t y i s$ $a p o i n t d i s c o n t i n u i t y, a j u m p d i s c o n t i n u i t y, o r a v e r t i c a l a s y m t o t e$

Question Number 73567 Answers: 0 Comments: 2

Determine the value of a and b fir which the function f,defined by f(x) = { ((−2sinx, x < −(π/2))),((asinx + b,−(π/2) ≤ x < (π/2))),((cosx, x > (π/2))) :} is continouos

$D e t e r m i n e t h e v a l u e o f a a n d b f i r w h i c h t h e f u n c t i o n f, d e f i n e d b y$ $f (x) = {\begin{cases} - 2 s i n x, x < - \frac{π}{2} \\ a s i n x + b, - \frac{π}{2} ⩽ x < \frac{π}{2} \\ c o s x, x > \frac{π}{2} \end{cases}$ $i s c o n t i n o u o s$

Question Number 73566 Answers: 0 Comments: 3

show that f(x) = ∣x∣ is not differentiable at x=0, where ∣x∣ denotes he absolute value function

$s h o w t h a t f (x) = ∣ x ∣ i s n o t d i f f e r e n t i a b l e a t x = 0, w h e r e ∣ x ∣$ $d e n o t e s h e a b s o l u t e v a l u e f u n c t i o n$

Question Number 73565 Answers: 0 Comments: 2

investigate the continuity of f ,given by f: x → { ((1−x, if x<1)),((0,if x =1)),((x^2 −3x + 2,if x >1)) :} at the point x =1

$i n v e s t i g a t e t h e c o n t i n u i t y o f f, g i v e n b y$ $f : x \to {\begin{cases} 1 - x, i f x < 1 \\ 0, i f x = 1 \\ x^{2} - 3 x + 2, i f x > 1 \end{cases}$ $a t t h e p o i n t x = 1$

Question Number 73561 Answers: 1 Comments: 0

find the value of λ for which f : x → { ((2λ − x, if x < 1)),((λ^2 + x −1, if x > 1)) :} has a limit as x→ 1

$f i n d t h e v a l u e o f λ f o r w h i c h$ $f : x \to {\begin{cases} 2 λ - x, i f x < 1 \\ λ^{2} + x - 1, i f x > 1 \end{cases}$ $h a s a l i m i t a s x \to 1$

Question Number 73560 Answers: 1 Comments: 1

prove that (1−itanθ)/(i+cotθ)=itanθ pleas sir help me?

$p r o v e t h a t (1 - i t a n θ) / (i + c o t θ) = i t a n θ$ $p l e a s s i r h e l p m e ?$

Question Number 73555 Answers: 1 Comments: 4

find a) Lim_(x→−∞) ((ln(1+e^x ))/e^x ) b) lim_(x→+∞) ((√(x^2 + 3x)) −x) c) lim_(x→0) (√x) ln(sinx) d) lim_(x→+∞) ((e^(2x+1) −e^x )/(x^2 −x−1)) e) lim_(x→−∞) [(√(1−xe^x )) ]

$f i n d$ $a) \underset{x \to - \infty}{L i m} \frac{l n (1 + e^{x})}{e^{x}}$ $b) \underset{x \to + \infty}{l i m} (\sqrt{x^{2} + 3 x} - x)$ $c) \underset{x \to 0}{l i m} \sqrt{x} l n (s i n x)$ $d) \underset{x \to + \infty}{l i m} \frac{e^{2 x + 1} - e^{x}}{x^{2} - x - 1}$ $e) \underset{x \to - \infty}{l i m} [\sqrt{1 - {x e}^{x}}]$

Question Number 73553 Answers: 1 Comments: 0

give: a,b,c>0 if a∣b and b∣c prove : a∣c

$give : a, b, c > 0$ $if a ∣ b and b ∣ c$ $prove : a ∣ c$

Question Number 73552 Answers: 1 Comments: 1

evaluate Lim_(x→+∞) xln (((x+1)/x))

$e v a l u a t e$ $\underset{x \to + \infty}{L i m} x l n (\frac{x + 1}{x})$

Question Number 73551 Answers: 1 Comments: 0

how many divisors does 38500 have?

$h o w m a n y d i v i s o r s d o e s 38500 h a v e ?$

Question Number 73550 Answers: 0 Comments: 0

solve 87x ≡ 3 (mod 5) and 55x ≡ 35 (mod 75)

$s o l v e$ $87 x \equiv 3 (m o d 5) a n d$ $55 x \equiv 35 (m o d 75)$

Question Number 73545 Answers: 1 Comments: 2

evaluate ∫lnx dx

$e v a l u a t e \int l n x d x$

Question Number 73544 Answers: 1 Comments: 0

expressf(θ)= 8cosθ −15sinθ in the form rcos(θ + α), where r>0 and α is a positive acute angle hence find the general solution of the equation 80cos θ −150sinθ = 13 the maximum and minimum value of (5/(f(θ) + 3))

$e x p r e s s f (θ) = 8 c o s θ - 15 s i n θ i n t h e f o r m$ $r c o s (θ + α), w h e r e r > 0 a n d α i s a p o s i t i v e a c u t e a n g l e$ $h e n c e$ $f i n d t h e g e n e r a l s o l u t i o n o f t h e e q u a t i o n$ $80 c o s θ - 150 s i n θ = 13$ $t h e m a x i m u m a n d m i n i m u m v a l u e o f \frac{5}{f (θ) + 3}$

Question Number 73542 Answers: 0 Comments: 0

Given that the function f(x)= x^3 is differentiable in the interval (−2,2), Use the mean value theorem to find the value of x for which the tangent to the curve is parallel to the chord through the point (−2,8) and (2,8)

$G i v e n t h a t t h e f u n c t i o n f (x) = x^{3} i s d i f f e r e n t i a b l e$ $i n t h e i n t e r v a l (- 2, 2), U s e t h e m e a n v a l u e t h e o r e m$ $t o f i n d t h e v a l u e o f x f o r w h i c h t h e t a n g e n t t o t h e c u r v e$ $i s p a r a l l e l t o t h e c h o r d t h r o u g h t h e p o i n t (- 2, 8) a n d (2, 8)$