Consider the following space curve { + y = 1, y? + 22 = 1. Find the equations of the tangent line and normal plane at the point (1,0, 1)

Q: and dy = Then d, and d are not 6- conjugate if Gis Non of these O D

A: Given d0 = -11   and   d1 = 56

Q: +oo (4 – x)" /n+ 5 9n · 7n Consider the power series n=1 Use Limit Comparison Test to show that the…

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Q: et Determine if the improper integral dx converges or diverges. (1 - e)2 If it converges, find its…

A: Test for converges of the definite Integral

Q: • Determine and draw the graph of the following equation in R3 : x2 + 212 + 2 8x + 12y – 2z + 35 = 0…

A: This is a problem of multi variable calculus, 3D geometry.

Q: 1 -1 Ob tai the Fruries Seriesi a Ans: fee= TT 2ntl Find; ab

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Q: Qz/Evaluate the complex integral: e? dz (z+ 1)(z – 2) where C is: a) The circle Iz| = 3 b) The…

A: 2 Given integral is ∮Cezz+1z−2dz. a We have to evaluate the given integral if Cis the circle z=3.…

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A: B is not the ancestor of J so first option incorrect C is the child of B therefore the second option…

Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: Example 7 Sketch the curves (a) r 1 (b) @ = 4. %3D in polar coordinates.

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Q: Use the convolution theorem to solve the following initial value problem 1, 01 y" + 2y y(0) = 0,…

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Q: -2-X Q1) Evaluate the integral S* dy dx using polar coordinate

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Q: (x -2) Given : an? + 4 (1.) Show that the reries converges conditionally when x - 1 ( 2.) Find the…

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Q: Exs Let PE-292]IR be function f(x)%={2 XEG -2 Showthat P3 R-integrable ornot?

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Q: The cost in dollars for removing p percent of pollutants from a river in Smith County is 72700p C(p)…

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Q: - 2T -T 271 a ftt)= Cos nt Fourier Series s'i n:1,3,5,... %3B findi a+ b+ C

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Q: +00 S (4 – x)" /n+ 5 9n · 7n n=1

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Q: Determine whether the following series is conve rgent or divergent. (1.) (use Integral Test.) (2.)…

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Q: c) Using the ower trianguler methed Kü)Using the upper frimgular methed elve; ース 2

A: The given augmented matrix is                             21111-212-18-22

Q: Evaluate : (a) L{e'u(t – 3)} (b) L{- 4e 3s (s-1)(s+3)

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Q: Q.2 An alternating current sfter passing through a rectifier has the form f(x) = losinx , OsxST = 0…

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Q: EXAMPLE 3 Evaluate fle Vx + z-ov, where E is the region bounded by the paraboloid y - x +z and the…

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Q: Question 2, Let x(t) be a differentiable function defined on (-1,0) satisfying the following…

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Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: Question 4 It is known that the general solution of the homogeneous differential equation dy + p(x)y…

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Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: Σ -1)2n Find a power series representation for (2n)! It is known that for all x ER, cos x = n=0 +00…

A: This is a problem of Taylor series.

Q: Determine whether the following series converge or diverge. 4+ cos? n •2 3n – Vñ Σ (5 – 4(In n)³)"…

A: Here we can use following test to check the convergence of the given series: (i) Limit comparison…

Q: Q2. Consider a unit square with vertices A (0, 2) B (1, 1) C (1, 2) and D (0, 0). Find the resultant…

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Q: Use double integral polar coordinates to find the area of the portion of the surface 3z = xy that…

A: Surface are of the surface z=fx,y is given by S=∫∫A 1+zx2+zy2 dA where A is the projection of the…

Q: VII. Let f(x) 1 — Зх 1 1 Find a power series representation for f(x) for all x E а. 3'3 (금) b. By…

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Q: For all x E R, e* = n=0 n! Express f (x) = x²e* as a power series. Find the third-degree Maclaurin…

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Q: Q2) Solve the D.E xdy + (2y-x*+ 3x)dx = 0

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Q: Show that if x is an integer, then gcd(x + 1, x2 – x + 1) divides 3. -

A: First, we find gcdx+1, x2-x+1 Now, factors of x+1 are x+1, 1 x2-x+1 is a quadratic equation of the…

Q: Find the value of a + b + c + d. (Answer must be an integer) The Differential Equation 2y"' + 3y" –…

A: Let us consider a differential equation L(D)(y)=Q(x) Determine the complementary solution by using…

Q: Let S be the surface defined by the vector function R(u, v) = (u cos v, u – v, u sin v) with u ER…

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Q: Q.3 An experiment gave the following values : v(ft/min) 350 t(min) It is known that v and t are…

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Q: fCxッサ) R: is the triangle cut from the first tuadrant by the line メャッ ! 2. R:y=4x-x ? and y=X

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Q: Given: 3z = xy Find f² + f +1 Option 1 Option 2 Option 3 O None of the choices

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Q: Find 3rd anall answen hould be sngle flaction Clowest kerm)

A: We have to approximate arccot (-1).

Q: Power set of empty set has exactly - subset. * One O Two Zero O Three O None from the choices Let…

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Q: Let X = {a, b, c, d, e}. Create a σ-algebra X from set X. Explain why it is a σ-algebra.

A: Given : The given set is  X = {a, b, c, d, e} To find : We have to create a σ-algebra from the set…

Q: (a) If an 2 0 for all n E N, then an does not converge conditionally. n=1 (b) If the power series >…

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Q: dy dv S.S; as sin ny dedy Cii)

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Q: (-1)"x2n (2n)! COS X = for all x E R. n=0 1. Let f(x) = cos(/x). Determine the power series…

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Q: Question 9 Let u(x, y) be the solution of the partial differential equation —и, —и+ уu,. х>0, у> 0,…

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Q: The task is to determine and sketch the domain of the function In (b – a? + 4) g(a,b) = V36 – 4a? –…

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Q: The student should answer the question below: The task is to show that the given function is…

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Q: . x(п) %3D (2)" и() + 3(-) и(п) — 4"u(-п - 1) |

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Q: 3- Vn n=1

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Q: Suppose f is continuous on the interval (0,3). Assume further that f(0)= -2 and f(-3)= 5. Also, lim…

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