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If y = \(\sqrt{sinx + \sqrt{sinx + \sqrt{sinx + ……. to \infty}}}\), find \(dy\over dx\).

Leave a Comment / Differentiation Questions, Maths Questions / By

Solution : Since by deleting a single term from an infinite series, it remains same. Therefore, the given function may be written as y = \(\sqrt{sin x + y}\) Squaring on both sides, \(\implies\)  \(y^2\)  = sin x + y By using differentiation of infinite series, Differentiating both sides with respect to x, 2y \(dy\over …

If y = \(\sqrt{sinx + \sqrt{sinx + \sqrt{sinx + ……. to \infty}}}\), find \(dy\over dx\). Read More »

Find \(dy\over dx\) where x = a{cos t + \({1\over 2} log tan^2 {t\over 2}\)} and y = a sin t

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Solution : We have, x = a{cos t + \({1\over 2} log tan^2 {t\over 2}\)} and y = a sin t \(\implies\) x = a{cos t + \({1\over 2} \times 2 log tan{t\over 2}\)} and y = a sin t \(\implies\) x = a{cos t + {\(log tan{t\over 2}\)} and y = a sin t …

Find \(dy\over dx\) where x = a{cos t + \({1\over 2} log tan^2 {t\over 2}\)} and y = a sin t Read More »

What is the integration of \(e^x\) ?

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Solution : The integration of \(e^x\) with respect to x is \(e^x\) + C. Since \(d\over dx\) \(e^x\) = \(e^x\) dx On integrating both sides, we get \(\int\) \(e^x\) dx = \(e^x\) Hence, the integration of \(e^x\) is \(e^x\) + C

Find the determinant of A = \(\begin{bmatrix} 3 & -2 & 4 \\ 1 & 2 & 1 \\ 0 & 1 & -1 \end{bmatrix}\).

Leave a Comment / Determinant Questions, Maths Questions / By

Solution : | A | = \(\begin{vmatrix} 3 & -2 & 4 \\ 1 & 2 & 1 \\ 0 & 1 & -1 \end{vmatrix}\) By using 3×3 determinant formula, \(\implies\) | A | = \(3\begin{vmatrix} 2 & 1 \\ 1 & -1 \end{vmatrix}\) – \((-2)\begin{vmatrix} 1 & 1 \\ 0 & -1 \end{vmatrix}\) + …

Find the determinant of A = \(\begin{bmatrix} 3 & -2 & 4 \\ 1 & 2 & 1 \\ 0 & 1 & -1 \end{bmatrix}\). Read More »

What is walli’s formula in integration ?

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Walli’s Formula : If m,n \(\in\) N & m, n \(\ge\) 2, then (a)  \(\int_{0}^{\pi/2}\) \(sin^nx\)dx = \(\int_{0}^{\pi/2}\) \(cos^nx\)dx = \((n-1)(n-3)….(1 or 2)\over {n(n-2)….(1 or 2)}\) K where K = \(\begin{cases} \pi/2 & \text{if n is even}\ \\ 1 & \text{if n is odd}\ \end{cases}\) (b)  \(sin^nx.cos^mx\)dx = \([(n-1)(n-3)….(1 or 2)][(m-1)(m-3)….(1 or 2)]\over {(m+n)(m+n-2)(m+n-4)….(1 or …

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What is Newton Leibnitz formula with Examples ?

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Newton Leibnitz formula If h(x) and g(x) are differentiable functions of x then, \(d\over dx\) \(\int_{g(x)}^{h(x)}\) f(t)dt = f[h(x)].h'(x) – f[g(x)].g'(x) Example : Evaluate \(d\over dt\) \(\int_{t^2}^{t^3}\) \(1\over log x\) dx Solution : We have, \(d\over dt\) \(\int_{t^2}^{t^3}\) \(1\over log x\) dx = \(1\over log t^3\) \(d\over dt\) \((t^3)\) – \(1\over log t^2\) \(d\over dt\) …

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Equation of Pair of Tangents to a Circle

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Here you will learn what is the equation of pair of tangents to a circle from an external point with example. Let’s begin – Equation of Pair of Tangents to a Circle Let the equation of circle S = \(x^2\) + \(y^2\) – \(a^2\) and P(\(x_1,y_1\)) is any point outside the circle. From the point …

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