Find the limit of each of the following sequences, using L'Hopital's rule when appropriate. √n Vn+1

Q: Where Given the vectors 2 = ( 2,-1, 3), B = PQ P (1, 1, 1) and Q (5,1, -1) and C = T J + 3R . • Find…

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Q: Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an…

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Q: So the system of equations by using the inverse of the coefficient matrix if it exists and by the…

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Q: Which of the following is NOT true about the linearity of differential equations? O A. Which of the…

A: Given query is to find the incorrect statment for liner differential equations.

Q: 5 5 Suppose ff(x) dx = 25, f f(x)dx s., $ f(x)d. 3 0 the following: a. 0 3 (5f(x) - 6g(x) + 4h(x))dx…

A: The basics of integration must be cleared in order to attempt this question. Rest of things are…

Q: Find the area between the curves (Hint: Your answer will be in terms of a.) The area is f(x)=x and…

A: area is=a3/6

Q: Let f(x) = 4x + 4 6x + 7 Determine (fof)(x).

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.…

A: degree=3

Q: If f (x) = x2 - 2x, find f (a + 1) and f (a + 2).

A: Given fucnction, fx=x2-2x

Q: the space curve (t) = (2t, t², 2t)

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Q: (a) J x² dx 3x + 2 x + 7 (b) 6) [ √2+1 da dx

A: Since multiple questions are asked, I am answering first question

Q: Which of the following equations can be made into a linear differential equation? OA. (x² + xy)dy -…

A: Option D

Q: The function s(t) describes the motion of a particle along a line. s(t) = t3 − 10t2 + 32t − 230…

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Q: † (OM_ON) - . If = -3, O A. e5 U O E. e-5 y5 y -5 then what is the integrating factor? None of the…

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Q: What is a suitable integrating factor that can be used to solve the equation dy dx O A. e B. 3 ex C.…

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Q: Which of the following is a non-homogeneous function? O tan³y/x xLnx − xlny x³ − xy + y² 3 2 - (y² +…

A: function f(x, y), if it can be written  by writing x = kx, and y = ky to form a new function f(kx,…

Q: Which of the equations below is a second order nonlinear differe O A. 2 dy |x²y- (1 - dx)² = e ²x O…

A: We have to choose the correct option from the given options according to the given information

Q: 17. Find the limit. x+5 lim 2 X-5x + 6x + 5 x+5 lim 2 x-5x + 6x +5 (Type an integer or a simplified…

A: Factorise the denominator x2+6x+5 and cancell the common factor of numerator and denominator.

Q: Solve the initial value problem y' ○ In (y) + In (1+x²) = ln (2) ○ In (y) = In (1+x²) + ln (2)…

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Q: The rate of change of the variable y in terms of another variable t is equal to the expression 5t4 -…

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Q: - Let 3x² + 1 13 10x - 7 ermine if f(x) is continuous at x = 2 by computing limit: f(x) = x 2

A: Given query is to find function is continuous or not on x = 2.

Q: Given f(x) = 4x¹n (x) " f'(9) _ answer the following:

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Q: Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an…

A: Given query is to apply sine law and complete the triangle.

Q: The integrating factor (IF) of the equation y' - 2ycot2x O A. sin2x O B. cot2x O C. Lnsin2x O D. E.…

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Q: The integrating factor (IF) of the equation: (2x³y² + 4x²y + 2xy² + xy4 + 2y)dx + (2y³ + 2x²y +…

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Q: Which among the choices is the same as the differential equation dP -= P(C₁-C₂P)? dt

A: Which of the following choices is the same as the differential equation.

Q: 38. Critical Thinking How many students receive each grade? Each student receives a grade of A, B,…

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Q: Another model for a growth function for a limited population is given by the Gompertz function,…

A: The givne growth function for the limited population is dpdt=clnkpp…

Q: 5. Show that dy ay of dx of arccosx -1 √1-x²

A: Given that dydx of arccosx=-11-x2 We have to prove this derivative.

Q: Find the present value of $4000 payable at the end of 4 years, if money may be invested at 8% with…

A: The amount $4000 payable at the end of 4 years, the money invested at 8% with interest compounded…

Q: Which of the following is a non-homogeneous function? tan³y/x OxLnx-xLny O x³ − xy + y² (y² + v²)³/2…

A: homogenous function is f( tx,ty ) = t^n f(x,y) option a) f(x,y) = tan (3y/x) now,…

Q: Which of the following equations can be made into a linear differential equation? O A. (x² + xy)dy -…

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Q: b = PQ Given the vectors a = (2,-1, 3), P(1,1,1) and Q (5,1,-1) and Z = T J + 3R Where ● Find the…

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Q: A solid lies between planes perpendicular to the x-axis at x = 0 and x = 18. The cross-sections…

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Q: b) Find the area of the region described. The region inside the rose r = 2a cos 2β and outside the…

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Q: The integrating factor (IF) of the equation y' - 2ycot2x = 1-2xcot2x - 2csc2x

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Q: Given the vectors à = (2, -1,3), b = PQ where P(1, 1, 1) and Q (5, 1, −1) and Ĉ=i+j+ 3k. Find a)…

A: Given the vectors a→=2, -1, 3, b→=PQ→ where P1, 1, 1 and Q5, 1, -1and c→=i→+j→+3k→.To find 7b→-3c→

Q: sin t t lim R t-

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Q: fies a(t) = −9.8 + mv(t)², where v(t) is velocity, negative since the object is falling, and k is a…

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Q: The voltage V in a simple electrical circuit is slowly decreasing as the battery wears out. The…

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Q: dy Which of the following is TRUE about the differential equation x +y dx A. The equation is…

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Q: find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A: Given expression, y=x3-3x2+4 P (2,0)

Q: Evaluate the following integral. 9 4 dx 1-√√x

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Q: Let ƒ(x) = x/x - 2. Find a function y = g(x) so that (ƒ ∘ g)(x) = x.

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Q: Question 2 Solve for the value of C in the equation: dy − (y + xy5)dx = 0 when y(0) = 1 A. 1/4 B.…

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Q: aluate the integral. [29 tan 29 tan 5x sec 4x dx

A: The given integral is  ∫29tan5xsec4xdx

Q: Find the y-coordinate of the point (a + 1, ?) if this point lies on the graph of the function f (x)…

A: Given: f(x) = x3 The points are: x = a+1 y =? Formula Used: a+b3 = a3+3a2b+3ab2+b3

Q: Find a polar equation for the curve represented by the given Cartesian equation. x + y = 4 2√2 sin…

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Q: Solve for the value of C in the equation: O A. 1 OB. 2 O C.3 O D.4 O E. None of the Choices alt + dx…

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Q: Use synthetic division to determine if the given value for k is a zero of this polynomial. If not,…

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