Question

Define Taykor's Eyansion of tan-¹xy about the point (1,-1) up to second degree tenns. llence Coupute f(0.9,-1.2)

Answer 1

To find Taylor's expansion of tan-1(xy) about the point (1,-1) up to the second degree terms, we need to use the formula for Taylor's expansion. Let's calculate f(0.9,-1.2) using this expansion.

Step-by-step explanation:

To find Taylor's expansion of tan-1(xy) about the point (1,-1) up to the second degree terms, we need to use the formula for Taylor's expansion:

Taylor's expansion:

f(x) = f(a) + f'(a)(x-a) + (1/2!)f''(a)(x-a)2 + ... + (1/n!) f(n)(a)(x-a)n

In this case, the function is tan-1(xy) and the point is (1,-1). We want to expand up to the second degree terms, so we will consider the terms up to (x-a)2.

Let's calculate f(0.9,-1.2) using this expansion:

f(0.9,-1.2) = f(1,-1) + f'(1,-1)(0.9-1) + (1/2!)f''(1,-1)(0.9-1)2

Now, we need to find the values of the function and its derivatives at (1,-1) in order to complete the calculation.