4-x III. Evaluate dx. V16-x2

Q: Find the second-order partial derivatives of the function. Show that the mixed partial derivatives…

A: Given: Now, fxx=∂2∂ x2x5+x2y2+y5+x+y    =∂ ∂ x5x4+2xy2+1    =20x3+2y2 fyy=∂2∂ y2x5+x2y2+y5+x+y…

Q: Find the polar equation of a line parallel to the line r cos (0 = 1 and lying at a distance d = 5…

A: The given line is: rcosθ-π5=1. A line parallel to it, will be of the form: rcosθ-π5=k

Q: JV-x² + 4x+5 Consider dx. Using trigonometric substitution, what is the integral form in terms of 0?

A: We have to determine  integral form of given question

Q: 3r + cos a 2. Use Squeeze Theorem to evaluate lim 1-00 V1+ x² – 5x

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Q: ind the area and the circumference of a circle with diameter 6 m. Ise the value 3.14 for a, and do…

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Q: Let C be a curve that is defined by x = 4 sin t and y = cos t, t e [0, 27). Determine (a) the time…

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Q: Solve the following problems. 1. Name and sketch the graph of y² = z in R³. II.

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Q: Find the saddle point/s of the function f(x,y) = x + y² +x²y+4 O a. (E ,-1) & (- 2 -1) O b.(4,0) &…

A: Let's find.

Q: Find the average rate of change of the function over the given interval. R(0) = 40 +1; [6,12] AR…

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Q: 5. Find two positive numbers whose sum is 10 and the sum of their squares is as small as possible.

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Q: Consider the following. 1 f(x) = 2x – 4 x2 y 4 3 y=2 x – 4 2 1 X 8 (a) Write the integral that…

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Q: I. Evaluate 4x² + 4x + 5 dx

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Q: S tan5 x dx O 1/4 sec^2 x(sec^2 x - 1) - In Icosx |+ C 1/4 (sec^4 x - sec^2 x -In Icosx |)+ C O 1/4…

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Q: curve has the following parametric equations with parameter t. x=2t-1/2t and y=2t+1/2t. Find dy/dx…

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Q: 3x2 + 7x + 28 A f(x) Using partial fraction, evaluate x3 + x2 + 7x dX, the decomposed fraction is x2…

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Q: dx - [f(e)de find f(e) - S. (x² + x + 1) 2 Using Trigonometric Substitution O 3 sec? e 4 4 3 sec? e…

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Q: (1 + 2x)e*dx, Using integration by parts and letting Given: u= -1 - 2x, dv = f (x) dx, then the…

A: The given integral,     ∫0∞1+2xex dx

Q: cos. Given: tan x |dx. Using trigonometric transformation , the integral in terms of u is m ( u ™ )…

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Q: Integration by Parts Example 4. Evaluate In x dv,

A: The given integral is: I=∫lnxdx   As we know that; ddxlnx=1x

Q: 2n+1 5. Σ 'n°(n+1)² n=1

A: let  bn=1n3∑n=1∞1n3    is convergent   by p series  Recall ∑n=1∞1nP    is convergent  iff p>1

Q: Find an antiderivative of the function. (a) h(q) = sin(q) H(g) = (b) f(x) = 3eX F(x) =

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Q: dy 4у dx х (у-3)

A: Given query is to find the soly of the differential equation.

Q: Describe the graph of the equation. r = 7 cos ti – 18 sin t j+ k O An ellipse in the planex = 1,…

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Q: Determine the general equation of the plane Ω passing through the point P(1, -4, -5) and parallel to…

A: Given: 2x+4y-z=0 Normal vector of the given plane will be 2, 4, -1

Q: sin COS dx V 32 COS 35 5cos² + C O 32 COS 32 + 4 COS 4 口 32 cosS Ssin+2-c cos () + c 35 4 4 32 CoS 7…

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Q: 4. The surface described by the equation x2 + y + z² = 0 is a(an) (a) elliptic paraboloid symmetric…

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Q: Use the properties of infinite series and the fact that Σ 1 1. 1 and 4 5" n = 1 6' n = 1 5 to find…

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Q: AY Deternine the elative maxina and relative Minima, If any.

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Q: |sin(x)cos(2x)sin(3x) dx sin(3x)cos(3x), sin(2x)cos(2x) sin(2x) 12 8 8. + C 4 sin(6x) sin(2x),…

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Q: 3(x + 2)\/1 (x+2)² Which of the following is *+2) + arcsin 9 +C equal to? arcsin (z + 2) + (x + 2)v5…

A: Given that,     92arcsinx+22+3x+21-x+2292+C

Q: |v|dt. Then find the Find the arc length parameter along the curve from the point where t= 0 by…

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Q: Let A = (1, 0, 2) and B = (6, -2, 3). Find projaB.

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Q: Evaluate the definite integral 3e-0.05r dr by the following steps: (a) Determine the indefinite…

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Q: 2x+11 1 Consider f dx = x2+x-6 x-2 x+3 then evaluate S(-dx xp(* - 3 x+3

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Q: %3D Determine the speed along a parameterized path c(t) = (6 sin¬'(t), 3 tan¬(1)) at time t = 0…

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Q: Using Integration By Parts ∫ x^3 √(x^2+4) dx find uv - ∫ v du

A: To give a representation for integration by parts.

Q: (x² -2x9 dy Solve The firest orler oDe

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Q: TRUE OR FALSE. The curve defined by the polar equation r = 2 + 3 sin θ is symmetric with respect to…

A: To determine whether the given statement is true or false.

Q: x² –9 dx Given: r3

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Q: Given the equation below, find dy/dx* 6x^3+2x^30 y+y^4= 9 dy/dx= Now, find the equation of the…

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Q: Evaluate the definite integral. '5 3 9 Vx2 dx

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Q: -4 Vx²+4x-5 Consider 1 dx, using trigonometric substitution find x. x+2

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Q: V4-x2 aluate dy dx using pol 2x-x2 prdinates.

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Q: Using trigonometric substitution, what is dx ? A sec + C 2x2 Vx² – 9 +C sec-1 6x2 none of the…

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Q: Complete the following KenKen puzzle to determine what is represented by x and y?

A: The rules of KenKen puzzle is: Use each number only once per row, once per column. Cages with just…

Q: (cos x2) dx. Use integration by parts. 1.

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Q: Evaluate the surface integral. xz ds, S is the part of the plane 2x + 2y + z = 4 that lies in the…

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Q: 9. Evaluate limf(x) = {"_ (x – 2; x 3 %3D x-3 а. 1 b. -4 с. 3 d. Does not exist 10. Evaluate limf…

A: Our Aim is to evaluate the limit of the expression given below:-limx→3 f(x)=x-2 ; x≤3-4;…

Q: 1/2 The result of dx is F(b) – F(a), where F(a) and F(b) are real numbers. What is the value of F…

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