Question

Find
dy/dx
at x=1, when x= t logt and
y =(logt)/t

(a) 1
(b) -1
(c) -1/2
(d) 0​

Answer 1

Answer:

Step-by-step explanation:

(a) First (2,5) = 1 divides 11. so by Theorem 3.23, there are infinitely

many solutions. To find these solutions note that by Euclidean Algorithm

2(-2) +5 = 1 and so 2(-22) +5(11) = 11. Thus, I = -22 and y = 11 is a

particular solution. All solutions are given by

I = ro + (b/d)n=-22+5n, and y = 90 - (a/dl)n = 11 - 2n

(b) First (17.13) = 1 divides 100. so by Theorem 3.23, there are infinitely

many solutions. To find these solutions note that by Euclidean Algorithm

17(-3)+13(4) = 1 and so 17(–300) + 13(400) = 100. Thus, I = – 300 and

y = 400 is a particular solution. All solutions are given by

I = 10 + (b/d)n = -300+13n, and y = y0 - (a/d)n = 400 - 17n

(c) First (21.14) = 7 divides 147, so by Theorem 3.23, there are infinitely

many solutions. To find these solutions note that by Euclidean Algorithm

21+14(-1) = 7 and so 21(21)+14(-21) = 147. Thus, I = 21 and y = -21

is a particular solution. All solutions are given by

I = 10 + (b/d)n=21+ 2n, and y=yu - (a/d)n= -21 - 3n