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Question Number 12257 Answers: 1 Comments: 0

Question Number 12255 Answers: 2 Comments: 0

Question Number 12254 Answers: 0 Comments: 0

Question Number 12246 Answers: 1 Comments: 0

Let g(x) be an ininitely differentiable function , such that g(2x + 6) = g^′ (3x − 1) for all x. given that g(((44)/3)) = 33 . find g′′(8)

$$\mathrm{Let}\:\:\mathrm{g}\left(\mathrm{x}\right)\:\mathrm{be}\:\mathrm{an}\:\mathrm{ininitely}\:\mathrm{differentiable}\:\mathrm{function}\:,\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{g}\left(\mathrm{2x}\:+\:\mathrm{6}\right)\:=\:\mathrm{g}^{'} \left(\mathrm{3x}\:−\:\mathrm{1}\right)\:\mathrm{for}\:\mathrm{all}\:\mathrm{x}. \\ $$$$\mathrm{given}\:\mathrm{that}\:\:\mathrm{g}\left(\frac{\mathrm{44}}{\mathrm{3}}\right)\:=\:\mathrm{33}\:.\:\:\mathrm{find}\:\:\:\mathrm{g}''\left(\mathrm{8}\right) \\ $$

Question Number 12245 Answers: 1 Comments: 0

Solve the differential equation (dy/dx) = ((4x + 2y − 3)/(8x − 4y + 5))

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{4x}\:+\:\mathrm{2y}\:−\:\mathrm{3}}{\mathrm{8x}\:−\:\mathrm{4y}\:+\:\mathrm{5}} \\ $$

Question Number 12228 Answers: 2 Comments: 0

Solve the differential equation (dy/dx) = ((2xy)/(x^2 + y^2 ))

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{2xy}}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} } \\ $$

Question Number 12226 Answers: 2 Comments: 0

Find the nth term of this sequence 3, 18, 45, 84, 135 ...

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{this}\:\mathrm{sequence} \\ $$$$\mathrm{3},\:\mathrm{18},\:\mathrm{45},\:\mathrm{84},\:\mathrm{135}\:... \\ $$

Question Number 12218 Answers: 1 Comments: 3

5!! = ?

$$\mathrm{5}!!\:=\:? \\ $$

Question Number 12209 Answers: 1 Comments: 1

For all n ≥ 1 , n ∈ Z, prove that, p(n) : 4 + 8 + ... + 4n = 2n(n + 1)

$$\mathrm{For}\:\mathrm{all}\:\mathrm{n}\:\geqslant\:\mathrm{1}\:,\:\:\mathrm{n}\:\in\:\mathrm{Z},\:\:\mathrm{prove}\:\mathrm{that},\: \\ $$$$\mathrm{p}\left(\mathrm{n}\right)\::\:\mathrm{4}\:+\:\mathrm{8}\:+\:...\:+\:\mathrm{4n}\:=\:\mathrm{2n}\left(\mathrm{n}\:+\:\mathrm{1}\right) \\ $$

Question Number 12207 Answers: 0 Comments: 0

Multi−point ∮(x)=x^3 well be equal to the values of the function ant its harvest.

Question Number 12197 Answers: 0 Comments: 8

Question Number 12190 Answers: 1 Comments: 0

Show that, 0.9999999999999 ...... ∞ is equal to 1

$$\mathrm{Show}\:\mathrm{that},\:\:\mathrm{0}.\mathrm{9999999999999}\:......\:\infty\:\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{1} \\ $$

Question Number 12189 Answers: 1 Comments: 0

Find the fraction to the below deimal 4.4444444444444....... ∞

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{fraction}\:\mathrm{to}\:\mathrm{the}\:\mathrm{below}\:\mathrm{deimal} \\ $$$$\mathrm{4}.\mathrm{4444444444444}.......\:\infty \\ $$

Question Number 12185 Answers: 1 Comments: 0

A particle is moving with velocity v=K(yi^ +xj^ ) prove that y^2 =x^2 +constant

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{velocity} \\ $$$${v}={K}\left({y}\hat {{i}}+{x}\hat {{j}}\right) \\ $$$${prove}\:{that} \\ $$$${y}^{\mathrm{2}} ={x}^{\mathrm{2}} +{constant} \\ $$

Question Number 12201 Answers: 3 Comments: 0

∫(1/(sin(x)))dx

$$\int\frac{\mathrm{1}}{{sin}\left({x}\right)}{dx} \\ $$

Question Number 12291 Answers: 1 Comments: 0

Question Number 12181 Answers: 0 Comments: 0

The value of xyz is 15/2 or 18/5 according as the series a,x,y,z,b are in an A.P. or H.P., then ′a+b′ equals where a, b are +ve integers.

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:{xyz}\:\mathrm{is}\:\mathrm{15}/\mathrm{2}\:\mathrm{or}\:\mathrm{18}/\mathrm{5} \\ $$$$\mathrm{according}\:\mathrm{as}\:\mathrm{the}\:\mathrm{series}\:{a},{x},{y},{z},{b}\:\mathrm{are} \\ $$$$\mathrm{in}\:\mathrm{an}\:\mathrm{A}.\mathrm{P}.\:\mathrm{or}\:\mathrm{H}.\mathrm{P}.,\:\mathrm{then}\:'{a}+{b}'\:\mathrm{equals} \\ $$$$\mathrm{where}\:{a},\:{b}\:\mathrm{are}\:+\mathrm{ve}\:\mathrm{integers}. \\ $$

Question Number 12173 Answers: 2 Comments: 0

Prove that ∀x∈[1,2] ⇒ 1−x^2 ≤ x

$$\boldsymbol{{Prove}}\:\boldsymbol{{that}}\:\forall\boldsymbol{{x}}\in\left[\mathrm{1},\mathrm{2}\right] \\ $$$$\Rightarrow\:\mathrm{1}−\boldsymbol{{x}}^{\mathrm{2}} \:\leqslant\:\boldsymbol{{x}} \\ $$

Question Number 12171 Answers: 1 Comments: 0

∫x^2 ×sgn(2x)dx=?

$$\int\mathrm{x}^{\mathrm{2}} ×\mathrm{sgn}\left(\mathrm{2x}\right)\mathrm{dx}=? \\ $$

Question Number 12170 Answers: 1 Comments: 0

In any △ABC, 2(bc cos A+ca cos B+ab cos C) =

$$\mathrm{In}\:\mathrm{any}\:\bigtriangleup{ABC}, \\ $$$$\:\mathrm{2}\left({bc}\:\mathrm{cos}\:{A}+{ca}\:\mathrm{cos}\:{B}+{ab}\:\mathrm{cos}\:{C}\right)\:= \\ $$

Question Number 12169 Answers: 1 Comments: 0

If tan α equals the integral solution of the inequality 4x^2 −16x+15<0 and cos β equals to the slope of the bisector of the first quadrant, then sin (α+β) sin (α−β) is equal to

$$\mathrm{If}\:\:\mathrm{tan}\:\alpha\:\mathrm{equals}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{solution}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{inequality}\:\:\mathrm{4}{x}^{\mathrm{2}} −\mathrm{16}{x}+\mathrm{15}<\mathrm{0}\:\mathrm{and}\: \\ $$$$\mathrm{cos}\:\beta\:\:\mathrm{equals}\:\mathrm{to}\:\mathrm{the}\:\mathrm{slope}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bisector} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{quadrant},\:\mathrm{then}\: \\ $$$$\mathrm{sin}\:\left(\alpha+\beta\right)\:\mathrm{sin}\:\left(\alpha−\beta\right)\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 12161 Answers: 0 Comments: 2

Question Number 12160 Answers: 1 Comments: 0

Two angles of a triangle are cot^(−1) 2 and cot^(−1) 3. Then the third angle is

$$\mathrm{Two}\:\mathrm{angles}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{are}\:\mathrm{cot}^{−\mathrm{1}} \mathrm{2} \\ $$$$\mathrm{and}\:\mathrm{cot}^{−\mathrm{1}} \mathrm{3}.\:\mathrm{Then}\:\mathrm{the}\:\mathrm{third}\:\mathrm{angle}\:\mathrm{is} \\ $$

Question Number 12156 Answers: 1 Comments: 0

If the ratio of the students that pass a test to those that fail is in ratio 4:1, If 9 students were chosen at random, what is the probability that exactly 7 passed the test.

$$\mathrm{If}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{students}\:\mathrm{that}\:\mathrm{pass}\:\mathrm{a}\:\mathrm{test}\:\mathrm{to}\:\mathrm{those}\:\mathrm{that}\:\mathrm{fail}\:\mathrm{is}\:\mathrm{in}\:\mathrm{ratio}\:\mathrm{4}:\mathrm{1}, \\ $$$$\mathrm{If}\:\:\mathrm{9}\:\mathrm{students}\:\mathrm{were}\:\mathrm{chosen}\:\mathrm{at}\:\mathrm{random},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{exactly} \\ $$$$\mathrm{7}\:\mathrm{passed}\:\mathrm{the}\:\mathrm{test}. \\ $$

Question Number 12155 Answers: 1 Comments: 0

Find the 35th derivative of (2x^3 + 5x^4 )^(60)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{35th}\:\mathrm{derivative}\:\mathrm{of}\:\:\left(\mathrm{2x}^{\mathrm{3}} \:+\:\mathrm{5x}^{\mathrm{4}} \right)^{\mathrm{60}} \\ $$

Question Number 12148 Answers: 0 Comments: 13

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