Evaluate Lim x->inf (3x+4)/sqrt(2x2-5), if x = a(theta−sin theta) y = a(1−cos theta) Show that (1 + dy/dx)2 = cos2(theta/2). Given that (x+y)2 = xy+1 find d2y/dx2 in terms of x and y. Find the derivative of cos((1-x2)/(1+x2)).

Here are the solutions to the problems:

1. Evaluate $\lim_{x \to \infty} \frac{3x+4}{\sqrt{2x^2-5}}$

Step 1: Divide the numerator and the denominator by the highest power of $x$ in the denominator, which is $x$ (since $\sqrt{x^2} = x$ for $x \to \infty$).

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