Exam Question **Part 1:** Evaluate **Part 2:** Find the Maclaurin's se | Mathematics I 2077

Mathematics I207710 marksNumerical: Double integral and Maclaurin seriesMultiple integrals

Exam Question

Part 1: Evaluate $\int_{3}^{2} \int_{0}^{\frac{\pi}{2}} \left( y + y^{2} \cos x \right) \, dx \, dy$

Part 2: Find the Maclaurin's series for $\cos x$ and prove that it represents $\cos x$ for all $x$ . [5+5]

Exam Question

Part 1: Evaluate $$\int_{3}^{2} \int_{0}^{\frac{\pi}{2}} \left( y + y^{2} \cos x \right) , dx , dy$$

Part 2: Find the Maclaurin's series for $\cos x$ and prove that it represents $\cos x$ for all $x$. [5+5]

Part 1: Double integral $\int{3}^{2}\int{0}^{\pi/2}(y + y^2\cos x)\,dx\,dy$ - Outer limits (for $y$ ): from $3$ to $2$ - Inner limits (for $x$ ): from $0$ to $\pi/2$ Part 2: Find Maclaurin series for $\cos x$ and prove it represents $\cos x$ for all $x$ . --- The limits are literally $\int3^2$ , so...

Part 1: Double integral $$\int{3}^{2}\int{0}^{\pi/2}(y + y^2\cos x),dx,dy$$ - Outer limits (for $y$): from $3$ to $2$ - Inner limits (for $x$): from $0$ to $\pi/2$ Part 2: Find Maclaurin series for $\cos x$ and prove it represents $\cos x$ for all $x$. --- The limits are literally $\int3^2$, so...

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Exam Question **Part 1:** Evaluate **Part 2:** Find the Maclaurin's series for cos x and prove that it represents cos x for all x. [5+5]

Exam Question Part 1: Evaluate Part 2: Find the Maclaurin's series for cos x and prove that it represents cos x for all x. [5+5]