Explanation

To find the slope of the tangent to the curve y³x + y²x² = 6 at (2, 1), we'll use implicit differentiation:

Given: y³x + y²x² = 6

Differentiating both sides with respect to x:

y³ + x_3y²(dy/dx) + y²_2x + x²*2y(dy/dx) = 0

Rearranging terms to isolate dy/dx:

(3xy² + 2x²y)(dy/dx) = -y³ - 2xy²

dy/dx = (-y³ - 2xy²) / (3xy² + 2x²y)

Now, evaluating dy/dx at (2, 1):

dy/dx = (-(1)³ - 2_2_(1)²) / (3_2_(1)² + 2*(2)²*1)

= (-1 - 4) / (6 + 8)

= -5 / 14

Explanation

Since ln(x + 3) ≥ 0, we have:

x + 3 ≥ 1 (since ln(u) ≥ 0 when u ≥ 1)

x ≥ -2

Explanation

The hyperbolic tangent function tanh(y) is defined as:

tanh(y) = (e^y - e^(-y)) / (e^y + e^(-y))

Explanation

Ravenous means انتہائی بھوک یا لالچی

Voracious means ایک بہت بڑی بھوک یا کسی چیز کی خواہش کا ہونا

Explanation

Sedulity means کسی کے کام میں تندہی یا مستقل کوشش

Carelessness means توجہ یا کوشش کا فقدان

Explanation

Given y = x²/(1 + x²),

∫y dx = ∫[x²/(1 + x²)] dx = ∫[1 - 1/(1 + x²)] dx = x - arctan(x) + C.

Given ∫y dx = C + f, f = x - arctan(x).

x - 1 + 1/(x + 1)

Explanation

Venezuela Capital is Caracas.

Venezuela Currency is Bolivar Fuerte.

Venezuela official language is Spanish.

Venezuela located is in Continent South America.

Venezuela Primary Religion is Christianity.

Venezuela Head of Govt. is President – Juan Guaidó.

Venezuela Parliament called .

Tricks for Remember

RK13-12-2022

Explanation

Explanation

Explanation