Sketch the curve y = x2 + 1 with the guidelines of sketching. If z = x | Mathematics I 2079

Mathematics I207910 marksNumerical: curve sketching derivativeCurve sketching

Sketch the curve $y = x^2 + 1$ with the guidelines of sketching. If $z = xy^2 + y^3$ , $x = \sin t$ , $y = \cos t$ , find $\frac{dz}{dt}$ at $t = 0$ . [10+0]

Sketch the curve $y = x^2 + 1$ with the guidelines of sketching. If $z = xy^2 + y^3$, $x = \sin t$, $y = \cos t$, find $\frac{dz}{dt}$ at $t = 0$. [10+0]

Part 1: Curve $y = x^2 + 1$ Part 2: - $z = xy^2 + y^3$ - $x = \sin t$ , $y = \cos t$ - Evaluate $\dfrac{dz}{dt}$ at $t = 0$ --- 1. Domain: Polynomial, so domain is $(-\infty, \infty)$ . 2. Intercepts: - $y$ -intercept: $x=0 \Rightarrow y = 1$ , point $(0,1)$ . - $x$ -intercept:

Part 1: Curve $y = x^2 + 1$ Part 2: - $z = xy^2 + y^3$ - $x = \sin t$, $y = \cos t$ - Evaluate $\dfrac{dz}{dt}$ at $t = 0$ --- 1. Domain: Polynomial, so domain is $(-\infty, \infty)$. 2. Intercepts: - $y$-intercept: $x=0 \Rightarrow y = 1$, point $(0,1)$. - $x$-intercept:

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Sketch the curve y = x2 + 1 with the guidelines of sketching. If z = xy2 + y3, x = sin t, y = cos t, find fracdzdt at t = 0. [10+0]