What type of limacon is the graph of the polar equation given by r = √3+ cos 0? O Limacon with a loop Convex limacon O Cardiod Limacon with a dent

Q: 3x The directional derivative of f(x,y,z)=ln at the point P (2,0,-1) in the direction 1+yz z² from P…

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Q: 1. The integral can be rewritten as биз S= du u + 1 6u² S₁ -du u²+ 1 6u5 S; u³+1 f247du B. C. D. -du…

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Q: Which ONE of the following statements is CORRECT with regards to the sequences of real numbers? OA.…

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Q: (D^5-3D^4+8D^3+16D^2-9D-13)y=0 nonhomogeneous undetermined coefficients

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Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. The x-coordinate of the centroid of the…

A: Solution is given below:

Q: integrate * S(4√r – V√r² – 6√r³) dr 8 ·12 3 r³ – 2/4 r ² + C 5 35 r-ri-24r + C ² 35 24 3²-5r³+²+ C…

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Q: Consider the solid formed by the boundaries outside the elliptic parabo x² + y² = z and inside the…

A: Question is incomplete

Q: If u = ₁+₂y+z, where a₁, A2, A3 al constants and J²u J²u J²u น a +a+a = 1. Show that + + = U. მ2 მყ2…

A: This question is based on Partial diffrentiation.

Q: U= at ² w + 0х2 8² w dy² where 61, 62, 63 are constants and b₁ +6₂ +63 " 8² w + = W. az² Item 8.pdf…

A: Topic:- application of partial derivatives

Q: Which of the quantities is nearest to the value of * exp 0.003 1.001 cos(0.002) ? O 1 O 1.001 O…

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Q: The value of the integral in terms of u is? (a). 2u³ + 6u + Arctanu + C (c). 2u³-21n|u³+1| + C dx…

A: To evaluate: ∫dxx3+x Let I = ∫dxx3+x Assuming x=u6⇒dx = 6u5du

Q: Use polynomial long division to write 2x² + x³ 3x² + 4x-9 - = Q(x) + 1²+1 = p(x) 1²+1

A: To divide using the long division.

Q: fx ln x dx.

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Q: Evaluate the limit using L'Hopital's rule. Answer should be expressed as a whole number value, no…

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Q: dx Evaluate ·S- x1/2 + +x213 A none of the choices B С) ℗ D E using rationalizing substitution. 3 ln…

A: Let's evaluate given integral by rationalizing substitution.

Q: [CLO-3] The second derivative f"(x) of a function is given. Use this information to determine where…

A: Here, given that f''(x)=x2(x-7)(x-2)

Q: consider using rational

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Q: The region is bounded by y = x³, y = 2x + 4 and y = −1. The y - coordinate of the centroid of the…

A: Let's compute value of given a+b+c+d-4f(2)/g(2).

Q: Part II: Point Conversions 1. Convert (2,7) into a rectangular coordinate. 2. Convert (4,-4) into a…

A: I am attaching image so that you understand each and every step.

Q: Find the particular solution of y''-5y'=x-2 when x=0, y=0, y'=2

A: Given that that a non homogeneous differential equation and we find its solution.   Here i attached…

Q: The region is bounded by y = x³, y = 2x + 4 and y = −1. Then Area region = [ f(x) dx + √ f(x) dx +…

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Q: Find the derivative of the following using the differentiation rules. (x²-2x) (In x³-3 tan x) x√x y

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Q: Consider the region on the 1st quadrant bounded by y = √4x²,x and y- axes. If the region is revolved…

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Q: ∞ Consider the series (-1)" Which ONE of the following statements is CORRECT? n=1 3" OA. The series…

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Q: 2. The value of the integral in terms of u is? 2u³-21n|u³+1| + C 2u³-3u² +6u-6ln|u + 1| + C 6u+…

A: We know that integration of xn is xn+1/n+1.     Here i attached the solution of this question.

Q: 5 Given cos(8)= and the terminal side of 0 lies on the fourth quadrant. What is the value of cos 05…

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Q: Write an equation for the function graphed below. The y intercept is at (0,-0.5) 5 1 -7 -6 -5 -4 4 y…

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Q: x²-1 3. f(x) = -1;ƒ' (1) 2x+1

A: Solution is given below:

Q: provided. f6x³(2x5 + 2)dx

A: We expert are following guidelines we are supposed to do the first question. Please put another…

Q: -3x² 2(T T + 10 25)

A: Follow the procedure given below.

Q: * If z = f (x, y); then its total differential can be expressed as дz dydz date - ( 7 ), v + ( ;) -…

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Q: y"+y' = 0; y(0) = 0, y '(0) = 1 cost + sint t + cost + sint B) 1- e-t t-e-t O A) O D)

A: I am attaching image so that you understand each and every step.

Q: Use the shell method to find the volume of the solids generated by revolving the shaded region about…

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Q: Evaluate the following double integral over the given region R. [[ 2 ln(x + 1) (x + 1)y Use…

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Q: A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one…

A: We need to find equation.

Q: Question 10 The radius of convergence of the series (-1)" (n!) 0 3-6-9. (3n) Place) -(2x-1)" is…

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Q: The numerical value of the lim 818 n+3 nln (2) n+1 is equal to

A: We use L'Hôpital's rule to solve the limit.

Q: · ] x = 1 dA over a square region Using the transformations u=x-y and v=x+y to evaluate Rx+y with…

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Q: Find all points on the curve y = x3 + 2x2 -6x +5 where is the tangent is parallel to the line 2x + y…

A: The given curve y=x3+2x2-6x+5

Q: 4. O y=√3 x=3-y² D

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Q: Find: y = arctan = 1 O a. none of these O b. 0 с. O d. 177 O e.

A: Given;  y=tan-1[(x+1)/(x-1)] at x=1.

Q: day dx5 + day dx4 - 6 d³ y = 0 dx³

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Q: Ifv= U (x² + y² +2²), then 025 + 0 + 02 is dy² 0 0 01 1 O-1/2 O Other:

A: Here we have to do the partial differentiation of the given function.

Q: Find the volume of the solid generated by revolving the given plane area having the given boundaries…

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Q: Evaluate the following definite integrals. Note: Final answer should be expressed as a decimal, not…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: 1.ƒ(x) = 4x³ – 7x² + 2x − 8 -

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Q: Given the function f(x, y, z) = x ln(1 − z) + following and simplify your answers. a) | fx b) u fxz…

A: We can answer both the answer as below

Q: boy wishes to use 100 feet of fencing to enclose a rectangular garden. Determine the aximum possible…

A: Given query is to find maximum possible area.

Q: Evaluate the following double integral over the given region R. JS Ta 4 ln(y + 1) (x + 1)(y + 1) dA…

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Q: find the slope of the curve x = e^-tcost2t, y=e^-2tsin2t at the point t= 0

A: find out the slope of the curve at t=0