Basic Mathematics207710 marksNumerical: graph shifting and epsilon-deltaEpsilon-delta definition
Sketch the graph of the function f(x) = x2 Shifted vertically up to 1 and -2 units and horizontally up to 3 and -2 units. # Find the delta algebraically for the following functions. 1. limx to 5 sqrtx-1, and L = 2, epsilon = 1 2. limx to 2 (2x - 2), and L = 6, epsilon = 0.02 [5+5]
Sketch the graph of the function $f(x) = x^2$
Shifted vertically up to 1 and -2 units and horizontally up to 3 and -2 units.
Find the $\delta$ algebraically for the following functions.
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$\lim_{x \to 5} \sqrt{x-1}$, and $L = 2$, $\epsilon = 1$
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$\lim_{x \to 2} (2x - 2)$, and $L = 6$, $\epsilon = 0.02$
[5+5]
Part 1 (Sketching): Base function $f(x) = x^2$. - Vertical shifts: up 1 unit and down 2 units - Horizontal shifts: right 3 units and left 2 units Part 2 (Finding $\delta$): - Problem 1: $\lim{x \to 5} \sqrt{x-1}$, $L = 2$, $\epsilon = 1$ - Problem 2: $\lim{x \to 2} (2x - 2)$, stated $L = 6$,