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Question Number 39166 Answers: 1 Comments: 1

Find the value of k if (2,k) ,(3,4) and (6,4) are collinear. hence find the equation on the line 3i − j with the above points

$F i n d t h e v a l u e o f k i f$ $(2, k), (3, 4) a n d (6, 4) a r e$ $c o l l i n e a r .$ $h e n c e f i n d t h e e q u a t i o n o n$ $t h e l i n e 3 i - j w i t h t h e a b o v e$ $p o i n t s$

Question Number 39165 Answers: 0 Comments: 4

calculate ∫_0 ^∞ (dt/(1+t^(4 ) +t^6 ))

$c a l c u l a t e \int_{0}^{\infty} \frac{d t}{1 + t^{4} + t^{6}}$

Question Number 39170 Answers: 0 Comments: 0

Find the value of k if (d/dx)(f(x))= 6 when x = −1 and f(x) = 3x^3 − kx^2 + 1 if f(2) = 8 find one factor of f(x) and hence Evaluate lim_(x→∞) (f(x)).

$F i n d t h e v a l u e o f k i f$ $\frac{d}{d x} (f (x)) = 6 w h e n x = - 1$ $a n d f (x) = 3 x^{3} - {k x}^{2} + 1$ $i f f (2) = 8 f i n d o n e f a c t o r o f$ $f (x) a n d h e n c e E v a l u a t e$ $\underset{x \to \infty}{l i m} (f (x)) .$

Question Number 39156 Answers: 1 Comments: 0

Question Number 39142 Answers: 1 Comments: 0

F(x) = x^3 −9x^2 +24x+c=0 has three real and distinct roots α , β & γ . Q.1 → Possible value of c is : Q.2 → If [α]+[β]+[γ]= 8 then c is : Q.3 → If [α]+[β]+[γ]=7 then c is : Options for the above 3 Q. → a) (−20,−16) b) (−20,−18) c) (−18,−16) d) none of these. [.] = greatest integer function.

$F (x) = x^{3} - 9 x^{2} + 24 x + c = 0 h a s three$ $real and distinct roots α, β & γ .$ $Q . 1 \to Possible value of c is :$ $Q . 2 \to If [α] + [β] + [γ] = 8 then c is :$ $Q . 3 \to If [α] + [β] + [γ] = 7 then c is :$ $Options for the above 3 Q . \to$ $a) (- 20, - 16) b) (- 20, - 18)$ $c) (- 18, - 16) d) none of these .$ $[.] = greatest integer function .$

Question Number 39135 Answers: 1 Comments: 2

calculate A(λ) = ∫_0 ^λ ((ln(x+(√(1+x^2 ))))/(√(1+x^2 ))) dx 2) calculate ∫_0 ^1 ((ln(x+(√(1+x^2 ))))/(√(1+x^2 )))dx

$c a l c u l a t e A (λ) = \int_{0}^{λ} \frac{l n (x + \sqrt{1 + x^{2})}}{\sqrt{1 + x^{2}}} d x$ $2) c a l c u l a t e \int_{0}^{1} \frac{l n (x + \sqrt{1 + x^{2})}}{\sqrt{1 + x^{2}}} d x$

Question Number 39127 Answers: 0 Comments: 1

Given the lines l_1 : x + y = 5 and l_2 : y = 4x and l_3 ; 4x + y − 1 =0 show that l_(2 ) is perpendicular to l_3 . find the point coordinates if x + 2y = 5 is colliner to l_1

$G i v e n t h e l i n e s$ $l_{1} : x + y = 5 a n d l_{2} : y = 4 x$ $a n d l_{3}; 4 x + y - 1 = 0$ $s h o w t h a t l_{2} i s p e r p e n d i c u l a r$ $t o l_{3} .$ $f i n d t h e p o i n t c o o r d i n a t e s$ $i f x + 2 y = 5 i s c o l l i n e r t o l_{1}$

Question Number 39144 Answers: 1 Comments: 0

f(x) = 3x^3 − 2x + k has factor (x − 1) find the value of k. with these value evaluate a) (d/(dx ))(f(x)_ ) b) ∫_5 ^2 (f(x))

$f (x) = 3 x^{3} - 2 x + k h a s$ $f a c t o r (x - 1)$ $f i n d t h e v a l u e o f k .$ $w i t h t h e s e v a l u e$ $e v a l u a t e$ $a) \frac{d}{d x} (f {(x)}_{})$ $b) \int_{5}^{2} (f (x))$

Question Number 39121 Answers: 0 Comments: 5

Find domain of (1+(1/x))^x ? Also prove thatL_(x→0^+ ) (1+(1/x))^x = 1 ?

$Find domain of {(1 + \frac{1}{x})}^{x} ?$ $Also prove that \underset{x \to 0^{+}}{L} {(1 + \frac{1}{x})}^{x} = 1 ?$

Question Number 39120 Answers: 1 Comments: 1

let A_n = ∫_1 ^n (([(√(1+x^2 ))] −[x])/x^2 ) dx (n integr ≥1) 1) calculate A_n 2) find lim_(n→+∞) A_n

$l e t A_{n} = \int_{1}^{n} \frac{[\sqrt{1 + x^{2}}] - [x]}{x^{2}} d x (n i n t e g r ⩾ 1)$ $1) c a l c u l a t e A_{n}$ $2) f i n d {l i m}_{n \to + \infty} A_{n}$

Question Number 39119 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) ((x^2 cos(4x))/((x^2 +1)^2 ))dx

$c a l c u l a t e \int_{- \infty}^{+ \infty} \frac{x^{2} c o s (4 x)}{{(x^{2} + 1)}^{2}} d x$

Question Number 39104 Answers: 1 Comments: 1

Question Number 39089 Answers: 2 Comments: 1

Question Number 39078 Answers: 1 Comments: 2

Without using l′hopital find lim_(x→3) ((√(9−x^2 ))/(x−3))

$W i t h o u t u s i n g l^{'} h o p i t a l$ $f i n d \lim_{x \to 3} \frac{\sqrt{9 - x^{2}}}{x - 3}$

Question Number 39072 Answers: 2 Comments: 1

Question Number 39067 Answers: 2 Comments: 7

Question Number 39059 Answers: 1 Comments: 0

Question Number 39058 Answers: 1 Comments: 1

Question Number 39055 Answers: 1 Comments: 0

Question Number 39040 Answers: 0 Comments: 0

find F(x) = ∫_0 ^π ln(x^2 −2x sin(2θ) +1)dθ .

$f i n d F (x) = \int_{0}^{π} l n (x^{2} - 2 x s i n (2 θ) + 1) d θ .$

Question Number 39039 Answers: 0 Comments: 2

let f(x) =(1/(1+∣sinx∣)) (2π periodic even) developp f at fourier serie .

$l e t f (x) = \frac{1}{1 + ∣ s i n x ∣} (2 π p e r i o d i c e v e n)$ $d e v e l o p p f a t f o u r i e r s e r i e .$

Question Number 39038 Answers: 0 Comments: 2

let f(z) = (z/(z^2 −z+2)) developp f at integr serie.

$l e t f (z) = \frac{z}{z^{2} - z + 2}$ $d e v e l o p p f a t i n t e g r s e r i e .$

Question Number 39037 Answers: 0 Comments: 2

calculate F(x)=∫_0 ^(2π) ((cos(4t))/(x^2 −2x cost +1)) dt

$c a l c u l a t e F (x) = \int_{0}^{2 π} \frac{c o s (4 t)}{x^{2} - 2 x c o s t + 1} d t$

Question Number 39035 Answers: 0 Comments: 1

find f(t) =∫_0 ^∞ sin(x)e^(−t [x]) dx with t>0

$f i n d f (t) = \int_{0}^{\infty} s i n (x) e^{- t [x]} d x w i t h t > 0$

Question Number 39034 Answers: 0 Comments: 1

calculate interms of n A_n = ∫_0 ^(2π) ((cos(nx))/(cosx +sinx))dx and B_n = ∫_0 ^(2π) ((sin(nx))/(cosx +sinx))dx .

$c a l c u l a t e i n t e r m s o f n$ $A_{n} = \int_{0}^{2 π} \frac{c o s (n x)}{c o s x + s i n x} d x a n d B_{n} = \int_{0}^{2 π} \frac{s i n (n x)}{c o s x + s i n x} d x .$

Question Number 39033 Answers: 0 Comments: 2

calculate ∫_(−∞) ^(+∞) ((xsin(2x))/((1+x^2 )^2 ))dx

$c a l c u l a t e \int_{- \infty}^{+ \infty} \frac{x s i n (2 x)}{{(1 + x^{2})}^{2}} d x$

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