Are these correct by any chance? And I have no idea how to figure out the secant/tangent line. Sorry for the trouble!
+33661 2b. Slope = (x^3 - 8)/(x - 2)
2c. Use l'Hopital's rule: \(\lim_{x\rightarrow2}\frac{x^3-8}{x-2}\rightarrow \lim_{x\rightarrow2}\frac{3x^2}{1}=12\) where both numerator and denominator have been replaced by their respective derivatives.
2d. Tangent line: y = mx + c. m = 12 from part 2c, so 8 = 12*2 + c so c = 8 - 24 = -16
Hence y = 12x - 16
14a and 14b Look again more carefully!
14e Approaching zero from the negative side: Looks like it's tending to 0.
14f Approaching zero from the positive side: Looks like it's tending to +infinity
+33661 2b. Slope = (x^3 - 8)/(x - 2)
2c. Use l'Hopital's rule: \(\lim_{x\rightarrow2}\frac{x^3-8}{x-2}\rightarrow \lim_{x\rightarrow2}\frac{3x^2}{1}=12\) where both numerator and denominator have been replaced by their respective derivatives.
2d. Tangent line: y = mx + c. m = 12 from part 2c, so 8 = 12*2 + c so c = 8 - 24 = -16
Hence y = 12x - 16
14a and 14b Look again more carefully!
14e Approaching zero from the negative side: Looks like it's tending to 0.
14f Approaching zero from the positive side: Looks like it's tending to +infinity
