3. Prove that the set of rational numbers of the form p/2" for p,n E Z is dense in R. The goal of the next few exercises is to construct special functions which will be useful later when we perturb or change slightly a given function. These functions are called "bump functions." Define B(z) = { exp(-1/2?) if z > 0 %3D 05 z J! 4. Sketch the graph of B(z). 5. Prove that B'(0) = 0.

Q: $6. 26 21 25

A: Solution of the problem as follows

Q: Evaluate 4-3

A: For a negative exponent, we will use reciprocal first.

Q: च ( eXprs the unswer inter wisofUN, furf

A:

Q: $ 438 200 115 2 215 433 380 193 45

A: Arrange the given observations in ascending order. 40, 45,52,115,124,126,185,189,193,200,…

Q: 6.5 please

A: Hi! Thank you for posting the question. Since your question has more than three sub-parts, we have…

Q: Plot 3, - 12, and 9 on the number line. -10 -5 10

A: We need to draw numbers on number line.

Q: 367 58

A: Given: ×3675821286

Q: Add. 644, seven + 326, seven The sum is seven (Simplify your answer.)

A: To find  The sum

Q: 30 45

A: To find the length of the hypotenuse and adjacent sides of a triangle.

Q: Son tres preguntas

A: To determine the value of function using graph.

Q: List all the ways that you can arrange the letters A,B, and C

A:

Q: ex- 12

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

Q: 16,17,18

A:

Q: Select Delete 46 |3 6 4|9 9 | 3 6

A: Taken the image and done. G.

Q: Evaluate   1 - ( 4 . 3 - 2 + 2 )

A: We have to evaluate: 1 - ( 4 . 3 - 2 + 2 )

Q: Solve. 10 = 96

A: To solve10x=96

Q: Evaluate 0 b 0 10

A:

Q: $400 $250 $100

A: It is given that the chances of winning are good only if 4000 tickets were printed. Number of…

Q: 36 please

A: Given rt=cost i +sint j +2t k  ,  t=π3

Q: 100 %3D 41

A:

Q: R S 16 T. 15 30 Q RS %3D P.

A: Given : PS is parallel to QR TP = 15TS = 16PQ = 30

Q: Use the digits 3,7,8,9. Write all the 4-digit numbers greater than 7000 and less than 8000.  Order…

A:

Q: 92 -89 3

A: