7. Factor the following function completely, state the following key features and sketch a graph of the function: Degree (Even or Odd) Sign of Lead Coefficient f(x) 4 = x² − 7x³ + 5x² + 31x x-intercept(s) - 30 y-intercept End Behaviour

Q: . Solve the initial value problem. y' +y = e 12, y(0)= -1

A: We have to find out

Q: ) Find any relative(local) extrema and saddle points of f(x,y)=xª+yª-4xy+1.

A:

Q: 5. Consider the following function: f(x)= e* (3x³) a. Determine the critical points of such function…

A: For a function f( x ) , we can find  critical points by f'( x ) = 0  Inflection points by f''( x ) =…

Q: 10 Neville's method is used to approximate f (0.5), giving the following table. Po = 0 P1 = 2.8 xo =…

A:

Q: Use Partial Fractions to obtain the "Inverse Laplace Transform" the following given expressions.…

A: Let F(s) be the function then inverse Laplace transform   is defined as  L-1(F(s))=f(t) Also,…

Q: Evaluate the surface integral J F. ds for the given vector field F and the oriented surface S. In…

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Q: Show that the equation x6 + * – 99 = 0 has at most two real roots.

A:

Q: The differential equation which has y = C1a + C2x as its general solution is: (a) y" 4 y' + --- 2Y =…

A: Since, you have posted multiple questions, but according to guidelines we will solve first question…

Q: For the following power series, find the radius and interval of convergence: Σ n=1

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Q: Perform the indicated operation. 15) 7– 3j – (5 + 3j) + 12

A: Given expression, 7-3j-5+3j+12

Q: 3. This year college athletes around the nation began to be able to profit from their name, image,…

A: Hypothesis testing

Q: Suppose f(x,y)=xex. At the point (2,0), in what direction is the directional derivative maximized?

A:

Q: 1 is a zero of the polynomial P(x)= x³ – 3x* + 7x³ – 13x² + 12x – 4 of multiplicity (а) 3 (b) 5 (c)…

A: Let's find x value.

Q: 4. The duck population near a small lake can be modelled by the d(t) = 0.5(t² + 8) (t + 4) Where t…

A: given that , duck population function is given by :-d(t) = 0.5(t2+8)(t+4)where  t is time in years…

Q: Suppose W is the subspace of R“ satisfying the equation x1 + x2 + x3 + x4 : A. Find a basis for W-.…

A:

Q: and g are continuous functions on D), the area and g is given by A = (f(x) – g(x)) dx.

A: Given that: f and g are two functions.

Q: 15. Find the derivatives of the following functions: (a) = 20 sin 15x; (b) - tan' x: (c)-" c cos x…

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Q: Gamma Distribution Example: The time until a total of 3 people have entered the post office follows…

A:

Q: 3.) Evaluate the following limits : a) lim x-2 b) (x²-3x+2) x-2 3-√√x lim- X-4 X-9

A:

Q: 11. Suppose X1, X2, ... , Xn are i.i.d. from a distribution with pdf: f(x) = e°x-0–1 for x > e f (x)…

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Q: In Exercises 11-12, use the inversion algorithm to find the i verse of the matrix (if the inverse…

A: