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Functions and Limits
If f(x,y) = 3x + 2y and g(x,y) = x2 – y2 for all real numbers of x and y, then f(g(1,2)3) = ?
F(g(1,2)3) = 3(1-4) + 2(3) = -3
Which of the following numbers lie on the imaginary axis of the Argand diagram?
- 8 + 3i
- 0 + 3i
- 8 + oi
- None of the above
0 + 3i
Only B has no real part so its lies on the imaginary axis of the Argand diagram.
In a triangle ABC, A = 45o, then the value of (1 + cot B)(1 + cot C) is equal to?
Easiest way to solve such questions is to assume angles of triangle;
A = 45o
A + B + C = 180o
B + C = 180 – 45o = 135o
Let’s take, B = 90o & C = 45o
= (1 + cot 90o) (1 + cot 45o)
= (1 + 0) (1 + 1)
= 1 x 2 = 2