Q21&Q25As these are very easy questions so solve all two questions in the order to get positive feedbackPlease solve both questions correctly in 30 minutes and get the thumbs up please show neat and clean work for itBy hand solution needed 96 CHAPTER 1 The DerivativeCheck Your Understanding 1.5for x3for x-3.Let/(x)=EXERCISES 1.5Is the function, whose graph is drawn in Fig. 7. continuous at thefollowing values of x?-5-4 -3 -2 -1Figure 71. x 04. x .0017. x=010, x= .00115. f(x)=-1-6x-316. f(x)=Is the function, whose graph is drawn in Fig. 7. differentiable at thefollowing values of x?18. f(x)=(x+2(3x17. f(x)=1fxEx(2x-1Determine whether each of the following functions is continuousand/or differentiable at x = 1.13. f(x)=x²14. 500-¹for x2 for x19. f(x)=x-1020. f(x)=12. x-35. x=-2for 0sx<1for 1sx52x-18. x-3-11. x-202x-2for-1sxslfor 1 < x≤5value 1 when both inequalities are true, and it has value 0 otherwise. And, in that case,the inequality > I will have value 0. Hence, our formula for Y₁ takes on the value of(5/2).X-(1/2)when-1s X's 1 and, following the same rules, our formula takes on the value of(1/2)X-2 when X>1.for 0sxslfor 114 53. x=36. x-29. x=312. x-21. Is f(x) continuous at x-372. Is /(x) differentiable at x-37The functions in Exercises 21-26 are defined for all x except forone value of x. If possible, define f(x) at the exceptional point in away that makes f(x) continuous for all x.21. f(x)=²-7x+10x-5²+x-12x+4sở t22. f(x)=23. f(x)=Solutions can be found following the section exercises24. f(x)--25. f(x)=x577*4x+25x-5x-s(6 + x)²-36X0x26. f(x)-1973-19x-01x27. Computing Income Tax The tax that you pay to the federalgovernment is a percentage of your taxable income, which iswhat remains of your gross income after you subtract yourallowed deductions. In a recent year, there were five rates orbrackets for a single taxpayer, as shown in Table 1.Table 1 Single Taxpayer RatesBut Not OverAmount Over$0$27,050$27,050$65,550$65,550$136,750$136,750$297,350$297,350Tax Rate15%27.5%30.5%35.5%39,1%So, if you are single and your taxable income was lessthan $27,050, your tax is your taxable income times 15%(15). The maximum amount of tax that you will pay onyour income in this first bracket is 15% of $27,050, or(15) x 27,050=4057.50 dollars. If your taxable incomeis more than $27,050 but less than $65,550, your tax is$4057.50 plus 27.5% of the amount in excess of $27,050. So,for example, if your taxable income is $50,000, your tax is4057.5+275(50,000 -27,050) 4057.5+ 275 x 22,950 =$10,368.75. Let x denote your taxable income and 7(x)your tax.28,29

We have to discuss about continuity of the given function

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Math

Calculus

positive

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Functions And Their Graphs

Section2.4: A Library Of Parent Functions

Problem 47E: During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate...

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