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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) ?Pove that the the limit of f(×) sqrt(1+x) as x appraches 0 is 1. Use the espsilon delta definitionUse L' Hopital's to find the limit as x approaches positive infinity of: (e^(3x))/(x^(2)) I hope you have a nice day!
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- Q48, calculate the definite integrals using the limit of both right and left Riemann sums. Calculate the left Riemann sums two (2) ways.Find the Limit L. Then use the epsilon-delta definition to prove that the limit is L. lim( (2/3)multiply by x+ 9) as x approaches 1.(a) Express the area under the curve y =x4 +5x2 +xfrom 2 to 7 as a limit.(b) Use a computer algebra system to evaluate the sum inpart (a).(c) Use a computer algebra system to find the exact areaby evaluating the limit of the expression in part (b).
- Express the limit as a definite integral on the given interval. see pic for full prob answer correctlyUse the Fundamental Theorom of Calculus to write the number 26 as an integral. 1.) If I pick the lower limit a as 0, what is the function I would use? _______ 2.) Show your integral set up here: ________ 3.) Find the antiderivative of the function in #1: __________ 4.) Show work on how you used the fundamental theorem of Calculus to find the upper limit b. The b I found is: _________Compute the following limit. Think about the cases when it is quicker not to use L’Hôpital’s rule. Provide written explanation.