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- Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the set whose sum is the zero vector. (Use S1, S2, and S3, respectively, for the vectors in the set.) (0, 0) = S={(5, 2), (-1, 1), (4, 0)) Express the vector s₁ in the set as a linear combination of the vectors $2 and $3. 51= Need Help? Read It Watch It Submit AnswerIn order to find a local minimum or maximum of a function, how do we manipulate the fırst derivative? Make it equal to zero O Make it positive O Make it negative Make it equal to f(x)How do i solve for r in the equation: A=P(1+rt)
- Evaluate the integral. Check your answer by differentiating. (Remember the constant of integration.) (x4 − 9x2 + 2) dxput these numbers in T formA:IV > partial derivative + V - L "dxdy Recall that for a general function fx), the integral feldx representa the difference of the area below the curve y = f(x) but above the r-axis when f(x) 2 0, and the area above the 104 CHAPTER 3. MULTIPLE INTEGRALS eurve but below the r-axis when f(x)s0. Similarly, the double integral of any continuous funetion f(x, y) represents the difference of the volume below the surface z=f(x, y) but above the xy-plane when f(x,y) 20, and the valume above the surface but below the xy-plane when flz,y) s0. Thus, our method of double integration by means of iterated integrals can be used to evaluate the double integral of any continuous funetion over a rectangle, regardless of whether fix, y)20 or not. Exumple 3.3. Evaluate [ sintx+ y)dxdy. Solution: Note that f(x,y)= sin(r+y) is both positive and negative over the rectangle [0,) (0,2n1 We can still evaluate the double integral: sin(x + yldzdy = (-conlx + y)dy (-cos(y+)+ cos y)dy - - sin(y+n)+ sin y. --sin3r…