Chapter 5.6, Problem 36ES

24. What is the value of ¿4, where i 25. Simplify log2 (8). = −1? 26. If P(x) = x³- 2x² + 5x - 10, find P(2). 27. Solve for x: e2x = 7.

9. Solve the differential equation: 10. Find the general solution of dy + y = 0. dy 33 dx 3x².

3. Differentiate f(x) = x² sin(x). 4. Evaluate the limit: sin(2x) lim x

1. Solve for x in the equation: 2. If A = (1/3 2/) 4 x³-3x²+4=0 find the determinant of A.

3/4+1/2=

if a=2 and b=1 1) Calculate 49(B-1)2+7B−1AT+7ATB−1+(AT)2 2)Find a matrix C such that (B − 2C)-1=A 3) Find a non-diagonal matrix E ̸= B such that det(AB) = det(AE)

1.2.17. (!) Let G,, be the graph whose vertices are the permutations of (1,..., n}, with two permutations a₁, ..., a,, and b₁, ..., b, adjacent if they differ by interchanging a pair of adjacent entries (G3 shown below). Prove that G,, is connected. 132 123 213 312 321 231