Exercise 4:[Challenge] Letf be a function that is everywhere differentiable. Prove that f' has no jump dis- continuities or removable discontinuities. Remark: I consider this exercise important, since it shows that there exist many functions that are not the derivative of another function. We will show next quarter that every continuous function is the derivative of some function.

Q: 6+w=4

A: The give equation is 6 + w = 4To find the value of w.

Q: 3y² - 2y-1 (-)-5y²- 2y +6

A:

Q: Find &A if a-12 and b-7.

A:

Q: n is the same as 239 added to the product of 238 and z

A:

Q: (an)) ヘー 4n

A: Apply the ratio test

Q: 0*1=?

A: The product of zero(0) with any finite real number equal zero.  That is 0*n = 0, when n is a finite…

Q: VEX2 9

A: Use the substitution and solve the integral easily.

Q: n-6=5

A: Here we have to find the value of n =?  3n-6=5n

Q: 10+7=?

A:

Q: p2 sec? r³ dr

A:

Q: 12 R 10 5

A:

Q: 24 = 3 + y

A: We have to solve the given expression for y. The expression is 24=3+y.

Q: Y -2 -1 1 3 6

A: Given query is to find indicated limit.

Q: Rang lertex = (-7;3) qu'od

A: The quadratic function has vertex (-2,3) and a point on graph 1, 12

Q: To-42 5-2X-3 (6z) odz dy oe aly de

A:

Q: (-3)² ÷ 3 • (5 - 10 + -8)

A:

Q: ex- 12

A: Given: y=ex-12 we know that am-n=aman

Q: Find A. -6 4 (4A)-1 -2 1 A =

A:

Q: Find g C4

A: Here we have to find the value of 9C4.

Q: 7+9=?

A: We need to find the sum of 7 and 9

Q: 10+9=3p

A:

Q: 30 = 6 + z z =

A: Given : 30  = 6+z

Q: dx 4е2я — 8ет + 5

A: This question can be solved using the concept of special integrals.

Q: find 4 j! j30

A: Simply expand the summation and add all values after calculation.

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.