Verify Green's Theorem by evaluating both integrals dA [_v² dx + x² dy = [] (ON-OM) A ax ay for the given path. C: boundary of the region lying between the graphs of y = x and y = x² 1 √√√x² dx + x² dy = 30 X ƏN // (ON-ON) CIA - - 30 dA = əx ay X

Q: lim x →3 (x − 3) tan(9 — x²) sin²(2x - 6)

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Q: Find T(t) and N(t) at the given point. T(0)=(1,1,1) N(0) = (0, 2, 1) x = e cost, y = et sint, z=e¹;…

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Q: • 1/2 dx x2 15. 16. dx [²2/ x6

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Q: fe²x+Inx² sin x² dx = e2x cos x² dx

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Q: 18 Identify the center of the conic section whose equation is 5x 2 + 9y 2 - 80x + 54y + 221 = 0…

A: Solution is here

Q: 1. (1 - ху)ý + у2 + 3xy3 = 0

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Q: Use the formula ‹(t) = = 198 t7 k(t) : (4+121 +¹8) ²³/ = ||r' (t) x r"(t)|| r(t) = t²i+t¹¹j X to…

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Q: Find volume of the solid bounded by z = 0, f(x,y) = x² + y², x² + y² = 4², 10y = -6x and 13y = 8x…

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Q: 1. Evaluate the following limits. L'Hopital's rule is NOT allowed. 2x 3x lim x-2- (-²-2- -3X=42) x -…

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Q: 1+/ lim x-1 2x² + x1

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Q: 33. (a) L²₁ let - 11 dx r3

A: Since you have asked multiple questions in a single request we would be answering only the first…

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Q: Find the area under the curve y = Find the average value of y = 7x³ over the interval [0, 4]. 7x³…

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Q: 1. Identify the equations of all the linear asymptotes of f.

A: There are three different types of asymptotes for a function fx: (i) Horizontal asymptote: If we…

Q: +x+1 2x² +2+x³+x dx = [Aƒ'(x) − B ln(g(x)] + D, and if A=B<0, then f x+2 -2x + +5In(x + 2) + C 2 x²…

A: Solution of the problem as follows

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Q: a) Find Maclaurin series generated by the following function f(x) = e-3x by Test the following…

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am doing…

Q: Give the properties for the equation x 2 +y 2 + 4x + 6y - 12 = 0 Radius 5 2√3 4

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Q: Answer the following problems using the specified method up to four (4) iterations only. Round off…

A: Function f(x)=e-0.5x(4-x)-2Derivative of f(x)=f'(x)

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 3. lim (x-3) tan(9-x²)…

A: Formulas of limits which have been used are written in the solution

Q: 19 Give the properties for the equation 9x 2 + 16y 2 - 36x + 96y + 36 = 0 Major Axis 8 16 9

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Q: dx secx+1

A: First simply the equation Using Trigonometric identities.

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A: Given equationr=(4-3t)i-7tj

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j…

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Q: (D4 − 1)y = 0

A: D4-1y=0

Q: 19. TT/2 -π/2 sin 0 de 20. * sec² 0 de

A: 19 ∫-π/2π/2 sinθdθ [-cosθ ]-π/2π/2 0 - 0 =0 other way sin is odd function so also integration is = 0…

Q: Given the function C(a) = (x-4) (x + 6) (x - 1) its C-intercept is its x-intercepts are

A: Solution is given below:

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 9x2/3 dy = Need Help? Read It…

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Q: Give the properties for the equation x 2 +y 2 + 4x + 6y - 12 = 0 Range -8 ≤ y ≤ 2 -7 ≤ y ≤ 3 -2 ≤…

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 1 + ²/ 1. lim x12x² + x1

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Q: if any. Find the absolute extremum point (s) of f(x) = el-cosa on [-, ],

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Q: 3 answers. cas (x² + 2) = x - 240 cashy X ५१ where x>0 cot 1(3) 3 1. COS S = Cea

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Q: Sπ/4 x² dx (x²+4)5/2 (Use trigonometric substitution)

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allow 1+ 3/ 1. lim. 1 2x²+x-1

A: Given: limx→ -11+1x32x2+x-1

Q: Use differentials and the graph off to approximate the following. (Round your answers to three…

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Q: . Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 4 4. lim loga (x+3)…

A: limx→1-log12(x+3)1-cosh(cos-1x)=limx→1- log2-1(x+3)1-cosh(cos-1x)since, limx→af(x). g(x)=limx→a f(x)…

Q: Evaluate the double integral ₁+² (y + 2x) dy dx p1+z² -1/2 O 0.0892 0.0888 O 0.0982 0.0999 0.0882

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Q: Identify the center of the conic section whose equation is 4x 2 - 25y 2 - 8x - 100y - 196 = 0. (-1,…

A: We can identify the center as below.

Q: If y=7x²y+z³ +yz² A = y³ z² e^5x a_x + 4x4 zcosy a_y+ 2x4 CosySinz a_z. Find the following at point…

A: Given, ψ=7x2y+z3+yz2A=y3z2e5x ax+4x4z cosy ay+2x4cosy sinz az           Note: The expert is supposed…

Q: Describe the long run behavior of f(p) = (p+ 2)(p+ 4) (p + 5): As p →→ ∞, f(p) → ? ✓ As poo, f(p) →…

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Q: Y sinh(1) (use logarithmic differentiation) 3 (sec x)²/2[/cot-¹x]

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Q: if any. Find the absolute extremum point (s) of f(x) = el-cost on [-, π],

A: Given data÷

Q: 31. (a) 32. (a) 33. (a) 12x-1| dx √2 + x) dx e* - 1| dx L'i lex -3π/4 (b) cos x dx (b) [*/² | } −…

A: Given: ∫-11ex-1dx

Q: II. Determine if [x+1]. if x < -1 S x + 1 f(x) = 2 tanh (x+¹) if 1<x< 1 1-x In [cosh (x + 1) + sinh…

A: It is solved whether f(x) is continuous or not.

Q: Locate the absolute extrema of the function on the closed interval. f(t) = ₂, [3,5]

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Q: Find the volume generated by revolving the given bounded plane area about the line. Use shell…

A: Volume

Q: A 48 B 96 0 D 32 If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are…

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Q: y"+9y=2e³x

A: Given; y''+9y=2e3x So, we can also write as; D2+9y=2e3x So, the auxiliary equation is; m2+9=0

Q: The general solution of y' = Y can be written in the form = C

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Q: Suppose that a function f(x) satisfies the following properties, together with the table of signs…

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