-4x - 4, f(x) ) = { x ² + 2x - ²1₁ 1, x < -1 x ≥ −1

Q: Compute the partial sums S2, S4, and S6. S2 = S4 = S6 = 3 1.2 + 3 3 + 2.3 3.4 +...

A: First we find the sops of given sequence.

Q: Let T denote the Nth trapezoidal approximation to 0 x³ dx.

A: Integration of x3dx limit from 0 to 1  We have to find T3  .i.e 3rd trapezoidal approximation

Q: 2 X 2 [√³² L √ ² - ²³ √ x² + ²³² dy da dx 0 X

A: ∫0√2∫x4-x2x2+y2dydx

Q: ly the Ratio Test to determine convergence or divergence, or state that the lim n→∞ an+1 an n n² + 1…

A:

Q: Find the general antiderivative. Use c as the constant of integration. x 9 dx

A: ∫exex+9dx

Q: The integral [7 sin 7 sin(x) cos(x) dx can be evaluated in four different ways: (1) The substitution…

A: let H=∫7sin(x)cos(x)dx

Q: Use the Shell Method to calculate the volume of rotation, V, about the x-axis for the region…

A: By using the Shell Method to calculate the volume of rotation, V, about the  x-axis for the region…

Q: (b) Find the co-ordinates of the turning points of the following function: y = 3x4 - 16x³ + 24x² -…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Evaluate the definite integral. 1 e² + 8 o e² + 8z dz

A:

Q: Given u = a. 27 + 47 b. u c. u x d. lul V V [-4,4, 4] and = - [-5,6, 2] find

A: Addition of two vector formula and product rules

Q: Solve the given differential equation by separation of variables. (ex + 1)²e-y dx + (ex + 1)¹e-x dy…

A: We need to solve (e^y+1)^2 e^(-y)dx+(e^x+1)^4 e^(-x) dy=0.

Q: 7. In the two questions that follow, the function f(x)=b* is an exponential function. Think…

A:

Q: Consider the series n=1 3 n+ 3 Let Sn be the n-th partial sum; that is, Sn - n 3 i=1 i + 3

A:

Q: 7. Given = [-4,4,4] and ✓ = [-5,6, 2] find a. 2ū + 4v b. c. u x d. lul V V

A:

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

A:

Q: 1. From a piece of cardboard that is 24 cm by 48 cm, cut equal squares out of the comers. Foldup the…

A: Let side length x squares cut from each corner of cardboard Objective:-To find the maximum volume…

Q: Determine x = f(t) for dx (t² + 6t). dt = 6x + 6, t> 0; f(1) = 9.

A:

Q: 1. 2. Find f'(x) and f"(x). Determine the following Domain a. b. x and y intercepts t. The critical…

A: derivative calculated by differentiation with respect to x

Q: If f(x, y, z) = 7xy²z³ + arcsin(x√z), find fx [Hint: Which order of differentiation is easiest?]…

A: If fx, y, z=7xy2z3+arcsinxz, then to find fxzy.

Q: Given the function f(x) = -2x³ +96x + 1, determine the intervals where the function is increasing…

A:

Q: Use the chain rule to find and, where First the pieces: дz ?х ?х дя ду Əs = дz Ət || = And putting…

A:

Q: (c) Given equation r²+(2-1)² = 4 in the cylindrical coordinates. (1) Express the equation in…

A:

Q: Consider the series Find S4 and S4= S8 = S8 n=1 3 n+7 43 Let Sn be the n-th partial sum; that is, Sn…

A: Given:  We have  Sn = 3/n+ 7  , limit series n =1 to infinity

Q: (ii) (iii) Find the co-ordinates of the turning points of the following function: y = x³ - 6x² +5…

A: Given the equation, we need to find out the turning points of the curve and also where it has maxima…

Q: me Value Theorem, which of the following is true?   A) f(x) achieves a maximum f(c) and…

A: f(x)=x2

Q: Describe the translations performed on f(x) = log(x) to graph g(x) = log(x – 7) – 7. Select all…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 2 miles from the lift-off…

A: dθdt=0.1 rad/min In ∆ABC…

Q: 4) Suppose the velocity of an object is v(t) = 9t-t³, where v(t) is measured in feet per minute.…

A:

Q: Write the vector shown on the graph below as a linear combination of standard unit vectors i and j.…

A: Graph

Q: Without a calculator work out the value of 5632–1402 1128 – 1 10 4 Please share your mettrod.

A:

Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) =…

A: we have given velocity function v(t)=5t-9

Q: Biologists have noticed that the chirping of crickets of a certain species is related to…

A: T=Temperature in degree FahrenheitN=Number of chirps per minute

Q: Water flows from the bottom of a storage tank at a rate of r(t) = 300 - 6t liters per minute, where…

A: This is question of calculus  Here rate of change of water flow is given  Further calculation is…

Q: Compute 1. x²ex³dx.

A: ∫-∞0x2ex3dx

Q: (a) Verify that y=tan(x + c) is a one-parameter family of solutions of the differential equation y'…

A:

Q: Find the area of the triangle with (-1,1,-2), (-2,0,1), and (0, -2, -1) as vertices. The area of the…

A: Given: Vertices of a triangle are (-1,1,2),(-2,0,1),(0,-2,-1) We are required to: Find the area of…

Q: Q4/ For the following three matrices : k 4 k A= 0.5 2k 0.5 2 8 2k 1 3 B=m 2 1 m a- Find value of (k)…

A: Given: A=k4k0.52k0.5282k,B=13m21m,C=22161184432 We are required to: a. Find the value of k if A is a…

Q: Find the accumulated present value of an investment over a 7 year period if there is a continuous…

A:

Q: Given the function f(x) = −2x³ +96x +1, determine the intervals where the function is increasing and…

A: f(x)= -2x3+96x+1 We have to find interval of increasing or decreasing of function and also interval…

Q: 2. Find F'(x) if F(x) =tan(3x² + 2x). Solution: U= du dx 11 dy du dy dx 11

A: As per our company guidelines we are supposed to solve first question in different questions so…

Q: 4. Determine the 75th derivative of each of the following functions. f(x)=xe b) f(x) = 3 cos2x a)

A:

Q: Construct a related rates problem where the answer to said problem is 1.5 Please make the problem…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Evaluate the integral. म (3ex+ 5 sin(x)) dx

A:

Q: When an initial amount of money, A, in dollars, is invested into an account that earns interest…

A: Ft=A·ert     Ft=19000·e0.094·t   A.  For t = 9 Ft=19000·e0.094·t=19000·  e0.094·  9=44275.83

Q: =x²-2x-3 and the x-axis from x=1 to x=5?

A:

Q: √2 cos 0 + √2 sin 6, find the Cartesian equation of the tangent line v Given the polar curve r = to…

A: We need to find equation of tangent line.

Q: f(t) = t sin(at) 14. f(t) nat

A:

Q: The equation for the price of a television, based on the demand, is P(x)=175-0.4e0.001x What should…

A: The equation for the price of television based on demand is P(x) = 175 -0.4e0.001x. Our task is to…

Q: 3) Factor the following polynomials: (a) 12x²y + 4xy² - 18ay (c) 2x² - 9x - 18 (d) 27y³ - 125 (b) d…

A: Given polynomials are : (a) 12x²y+4xy²-18xy ;  (b) d²-5d-66 (c) 2x²- 9x - 18 (d) 27y³-125 (e) 121x²…

Q: 61. an = nsin RIS n

A: We find the limit of given sequence.