Question 1 In this question we will estimate the value of tan (0.34x) using the linearization of f(I) = tan(NZ) at the nearby point : = 1/3. a) Compute the derivative of f at 1/3. f' (1/3) = FORMATTING: 1 is written pi, va is written sqrt(a). b) Write down the linearization L(x) of tan(xx) at x = 1/3. L(I) = FORMATTING: Give the exact value of all coefficients. c) Since 0.34 is near 1/3, we use the linear approximation of tan(x) found in (b) to estimate the value of tan(x) at x = 0.34. This gives tan(0.347) ~ Number FORMATTING: Round your answer to at least six decimal places. (You should check with your calculator and judge if this value is a good estimate.)Question 12 The goal of this exercise is to approximate the value of the definite integral _ (x- 1)da using a Riemann sum with left endpoints and 8 subintervals (i.e. using the Riemann sum Lg)- a) If you sub-divide the interval 5, 7) into 8 subintervals of equal length Ar, you get 8 subintervals of the form [I;_1, I;] whose union is the interval [5, 7]. Find the endpoints *0, $1, . .., Ig that define these 8 subintervals FORMATTING: To enter your answer, list the endpoints in the form [TO, $1, . .., Ig] including the square brackets [ ] and a comma (,) between endpoints. The endpoints should be exact numbers, ordered from left to right. Answer: [x0, $1, . . .,28] = b) Compute the exact value of each term ; = f(I;_])Ax of the Riemann sum Lg- FORMATTING: To enter your answer, list the terms in the form [t1, to,. . ., tg] including the square brackets [ ] and a comma () between consecutive terms. Each term must be an exact number. Answer: [1,t2, . . .,t;] = c) Compute the value of the Riemann sum Lg. Write your answer with an accuracy of two decimal places. Answer: Number- Question 13 Suppose that f is a function which is integrable on the entire real line, and that a and 6 are real numbers. Which of the following statements are true? Check each one that is true. O Sandx = (6- a) for any real number n. O If f(x)