In Problems 1-4, find a general solution
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- 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.arrow_forward9. Solve the differential equation: 10. Find the general solution of dy + y = 0. dy 33 dx 3x².arrow_forward3. Differentiate f(x) = x² sin(x). 4. Evaluate the limit: sin(2x) lim xarrow_forward
- 1. Solve for x in the equation: 2. If A = (1/3 2/) 4 x³-3x²+4=0 find the determinant of A.arrow_forwardListen ANALYZING RELATIONSHIPS Describe the x-values for which (a) f is increasing or decreasing, (b) f(x) > 0 and (c) f(x) <0. y Af -2 1 2 4x a. The function is increasing when and decreasing whenarrow_forwardBy forming the augmented matrix corresponding to this system of equations and usingGaussian elimination, find the values of t and u that imply the system:(i) is inconsistent.(ii) has infinitely many solutions.(iii) has a unique solutiona=2 b=1arrow_forward3/4+1/2=arrow_forwardif 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)arrow_forward1.2.17. (!) 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 231arrow_forwardProve that Pleas -- Pleas A collection, Alof countinoes Sunction on a toplogical spacex separetes Point from closed setsinx (f the set S" (V) for KEA and V open set in xx from base for Top onx. @If faixe A} is collection of countinuous fancton on a top space X Wich Separates Points from closed sets then the toplogy on x is weak Top logy.arrow_forwardWrite the equation line shown on the graph in slope, intercept form.arrow_forward1.2.15. (!) Let W be a closed walk of length at least 1 that does not contain a cycle. Prove that some edge of W repeats immediately (once in each direction).arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning