(b) (10%) The integral in (a) can be approximated by integrating the linear approximation of the integrand, i.e. let f(x) = 1 + x√1 - x^2 ≈ f(0) + f'(0) x Approximate ∫_-1^0 f(x) dx by evaluating ∫_-1^0 (f(0) + f'(0) x) dx

二、(50%)(所有題目請敘述計算過程，無計算過程不給分) 1. (10%) Let $A, B, C$ be $p \times q, m \times n, n \times p$ matrices and denote the $(i, j)$-entries of $A, B, C$ by $a_{ij}, b_{ij}, c_{ij}$ respectively. (a) (5%) Please write down the $(i,j)$-entry of the product $BCA$ in terms of Sigma notations (i.e. $\Sigma$).

(b) (10%) The integral in (a) can be approximated by integrating the linear approximation of the integrand, i.e. let

$$f(x) = \frac{1 + x}{\sqrt{1 - x^2}} \approx f(0) + f'(0) x$$

Approximate $\int_{-1}^0 f(x) \, dx$ by evaluating

$$\int_{-1}^0 (f(0) + f'(0) x) \, dx$$

相關申論題

相關試卷

(b) (10%) The integral in (a) can be approximated by integrating the linear approximation of the integrand, i.e. let $$f(x) = \frac{1 + x}{\sqrt{1 - x^2}} \approx f(0) + f'(0) x$$ Approximate $\int_{-1}^0 f(x) \, dx$ by evaluating $$\int_{-1}^0 (f(0) + f'(0) x) \, dx$$

相關申論題

相關試卷

(b) (10%) The integral in (a) can be approximated by integrating the linear approximation of the integrand, i.e. let

$$f(x) = \frac{1 + x}{\sqrt{1 - x^2}} \approx f(0) + f'(0) x$$

Approximate $\int_{-1}^0 f(x) \, dx$ by evaluating

$$\int_{-1}^0 (f(0) + f'(0) x) \, dx$$