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- If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?a. Graph h(x) = x2 cos (1/x3) to estimate limx-->0 h(x), zooming in on the origin as necessary. b. Confirm your estimate in part (a) with a proof.Find the slope of the tangent line to the parabola y=4x-x^2 at the point (1,3) 1) using the definition: m=lim->a f(x)-f(a)/x-a 2)using the equation: m=lim->0 f(a+h)-f(a)/h
- Because of their connection with secant lines, tangents, and instantaneous rates, limits of the form limh→0f(x+h)−f(x)h occur frequently in calculus. Evaluate this limit for the given value of x and function f. f(x)=x, x=19a) By graphing the function f(x)=(cos2x-cosx)/x2 and zooming in toward the point where the graphcrosses the -axis, estimate the value of lim x 0 f(x)We determined that l'Hospital's rule applies to the limit lim x→5 x2 − 10x + 25 x2 − 5x . Recall that when l'Hospital's rule applies, it states that lim x→a f(x) g(x) = lim x→a f '(x) g'(x) . Consequently, the next step is to take the derivative of the numerator and the denominator separately. d dx (x2 − 10x + 25) = d dx (x2 − 5x) =
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