Let z = 5 e5π i/4 Write z, z4, z⁹ and 2-2 in the form a + bi. z = 5 cos (5.) +/-5 sin(5.4) 4 Z4 z⁹ ||

Q: For y = xe^(-1/x), find the intervals of increase and decrease.

A: given function To find: the intervals of increase and decrease.

Q: Use a half-angle formula to find the exact value of tan 112.5°. tan 112.5° = √2 21 2 16 X 5

A:

Q: B) y(x) = 2+x

A: I have appended the formula used in solution procedure

Q: For the function f(x) = e¹x (6x - 2), use calculus to determine any interval(s) where the function…

A: Given: To Find: To determine the intervals of concave up, concave down and inflection point(s) of…

Q: The table gives the annual US emissions, H(t), of "super greenhouse gases," in millions of metric…

A:

Q: * Find the general Solution of :- - dy хе dxx New 1=Y, NOVIR VO

A: The given equation is; dy/dx = xex

Q: Question 4 Find the expression for the exact area of the surface obtained by rotating the curve…

A:

Q: Sketch the region R bounded by the curves y = e, y = 1, and x = 2, and find the coordinates of the…

A: We have to find the coordinates of the centroid.

Q: Evaluate F. dr along each path. (Hint: If F is conservative, the integration may be easier on an…

A:

Q: 5 Find f such that f'(x) = - √x f(16) = 49.

A: f′(x)=5x,f(16)=49

Q: Give two sets of polar coordinates for each of the points A-F in the figure. D E A 0 B F 3 G= T 4…

A: A graph of the polar coordinates of each points A-F are given.The aim is to find the polar…

Q: -2 -1 2+ 1 T 1 y=h(x) 2 True/False True or False: At every point where h'(c) is zero or does not…

A: To determine whether the following statement is true or false.At every point where  is zero or does…

Q: a. Find the linear approximating polynomial for the following function centered at the given point…

A:

Q: For t> 0 hours, let r(t) = 120 (1 - e 5 liters/hour hour, at which a car travels along a straight…

A:

Q: Find the general Solution of . T NOTINTOS dy dx = 2 x e x²²

A: dy/dx = x2

Q: 27. f(x) = 1 x² + 1 2 on [-1, 1)

A: Average value of f on [a,b]fave =1b−a∫abf(x)dx

Q: Determine if Find the limil if the sequence converges. 5-5n an 4 + Sn the sequence [an] converges or…

A:

Q: Using the graph below, sketch the graph of the function y = - f(x). -6 6 6

A: We have given the graph of f(x).The graph of the function y=-f(x) is the mirror image of the graph…

Q: Find the distance d (in the complex plane) between z = 2 + 7i and w = 11 - 10 i. d = √ (1)² + (9)² X

A:

Q: Let S be the hemisphere x² + y² + z² = 4, with z ≥ 0. Evaluate the surface integral JS₂ S z² ds: =…

A:

Q: Solve the following integration :- پیمرا Sin 2 x dx - Cos³x 2

A: The given integral is sin2x/(1-cos2x)

Q: Find the value of k that makes the antidifferentation formula true 1 - dx 3+ 7x k Inl3+ 7xl +C

A: To find the value of  that makes the antidifferentiation formula true.

Q: Express the limit as an integral. 4 lim (7(x)² - 2(x, ) ³) 4x over [0, 4] n→ ∞o Σ i = 1 dx

A:

Q: Check Answer/Save Find a(t): Step-By-Step Example Live Help Answer format: Enter the value (for…

A:

Q: A rectangle has its base on the x−axis and its upper vertices on the parabola y = 9−x^2. Find the…

A: Given that a rectangle has its base on the x−axis and its upper vertices on the parabola To…

Q: Estimate the area under the graph of f(x) = cos(x) from x = 0 to x = m/2. Use four approximating…

A:

Q: In each of the following functions is there any value of x where the function is discontinuous? If…

A:

Q: * Find the general Solution of dy dx = 4. x² ln x

A: The given differential equation is

Q: The vector field F(x, y) = (-y sin(xy), -x sin(xy)) is the gradient vector field of the function…

A: find r(t) at t=2,t=0

Q: Use Green's Theorem to evaluate the line integral. S 2xy dx + (x + y) dy C: boundary of the region…

A:

Q: Verify that the hypotheses of Rolle's Theorem are satisfied for fx √(x)= this interval that…

A:

Q: Please show steps. Derive the Laplace Transform of the function f(t) = t² (recall that the Laplace…

A: The given function is  To find:-The Laplace Transform of the given function

Q: Write an integral in the form A = the area of the region. Answers should be exact. As a suggestion,…

A:

Q: (a) Find the number a such that the line x = a bisects the area under the curve below. 1≤ x ≤4 a =…

A: The region under the curve,  To find the value of b such that the line bisects the area

Q: Use partial fractions to find the power series of the function: 52+74 (x − 9) (x + 8)

A: f(x)=5x+74(x−9)(x+8)5x+74(x−9)(x+8)=Ax−9+Bx+8

Q: The function f(x) = x³ + 5 is

A: f(x)=x3+5

Q: n's Theorem to evaluate the line integral (y - x) dx + (2x - y) dy C wen path. : boundary of the…

A:

Q: 2² y² Mikayla is a calculus student and needs to find the points on the ellipse + 81 1296 = 1 that…

A:

Q: 4. Let C(x) represent the cost, R(x) the revenue, and (x) the total profit, in dollars of producing…

A: Let C(x) represent the cost, R(x) the revenue and  the total profit, in dollars of producing x units…

Q: Prove that if g has an extremum value at x = c then f must have a tangent line parallel to the line…

A:

Q: Water is pumped out of a holding tank at a rate of 5 - 5e-0.11t liters/minute, where t is in minutes…

A:

Q: Find the slope of the tangent line to the parametric curve 3 cos (t) (y = 2 sin(t) X = at the point…

A:

Q: 10. An electric scooter manufacturer estimates that the cost C (in dollars) of producing x scooters…

A: Given, Where C is the cost of producing x scooters in dollars  We have to find the production level,…

Q: We turn now to the problem of finding area under a curve. Suppose we want to find the area between…

A: As per guidelines we can solve only 3 subparts if multiple subparts are posted. So I am solving…

Q: 9-30. Finding area Determine the area of the shaded region in the fol- lowing figures. 10.

A:

Q: Solve the following integration :- 3 S sin³x Sin³x cośx dx

A: The given integration is

Q: Verify that the hypotheses of the Mean-Value Theorem are satisfied for ƒ(x) = √√x + 16 on the…

A: To verify that the hypotheses of the Mean-Value Theorem are satisfiedfor  on the interval , and to…

Q: b) The rectangles in the graph below illustrate a ? The value of this Riemann sum is the vertical…

A: given function

Q: a) The rectangles in the graph below illustrate a The value of this Riemann sum is left endpoint…

A: given function

Q: D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item,…

A: