Question and Answers Forum
DifferentiationQuestion and Answers: Page 1
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Question and Answers Forum |
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DifferentiationQuestion and Answers: Page 1 |
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| Prove that ^3 (√((√5)+2)) −^3 (√((√5)−2)) =1 |
| without using LHopital rule evalute lim_(x→0) ((ln(1−x)−sin(x) )/(1−cox^2 (x))) |
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| u_n = Σ_(k=n+1) ^(2n) (1/k) and v_n = Σ_(k=n) ^(2n−1) (1/k) • show that u_n and v_n are adjacent use ln(x+1) ≤ x and x≤−ln(1−x) and • show that u_n ≤ Σ_(k=n+1) ^(2n) (ln(k)−ln(k−1)) hence deduce that u_n ≤ ln2 • show that v_n ≥ Σ_(k=n) ^(2n−1) (ln(k+1)−ln(k)) hence deduce that v_n ≥ln2 |
| Find the only function that satisfy the expression below: ((dy/dx))^2 = (d^2 y/dx^2 ) |
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| If f(x) = 2 + ∫_1 ^(−x^3 ) (√(2+u^2 )) du find the value of (d/dx) [f^(−1) (x)]_(x=2) |
| for the function z = xtan^(−1) ((y/x))+ysin^(−1) ((x/y))+2 then the value of x(∂z/∂x)+y(∂z/∂y)=? |
| For what values of k does the equation e^(kx) =3(√x) have only one solution in R? |
| Let y(x) be the solution of diff eq. y ′= ((cos x+y)/(cos x)) , y(0)=0 Find y((π/6)). |
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| If , H_n ^( −) =1−(1/2) +(1/3) −...+(((−1)^(n+1) )/n) prove that:Σ_(n=1) ^∞ ((H_n ^( − ) −ln(2))/n)=ln^2 (2) −−−−−−−−−− |
| If (√(1 − x^2 )) + (√(1 − y^2 )) = a(x − y) then prove that (dy/dx) = (√(((1 − y^2 )/(1 − x^2 )) )) . |
| If { ((f(x)=x^2 )),((g(x)=sin x)) :}, Then find (df/dg). |
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| How many real solutions does the equation x=sin3x have? |
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| If f(x)=(x!)∙(x!!)∙(x!!!) find (d/dx)(f(x))=? |
| I=∫_0 ^( ∞) ∫_0 ^( ∞) (( 1)/(1+ x^2 +y^2 +x^2 y^2 )) dxdy=? using polar system... |
| Donner l′e^ quivalence simple de I_n =∫^( 1) _( 0) (t^n /(t^n −t+1))dt |