Let p denote 3x E Z such that P(x)" and q denote dx E R such that P(x)". Ğive a simple definition for the predicate P(x) (but do not use "x 4 Z') so that q is true but n

Q: Find the antiderivative of: x*+1 (n+ 1)2 [(n + 1) In x – 1] if n± -1 x* In x dx = z (In x)² + c if n…

A: Find the anti derivative.

Q: az xdz + Y- = xy+z. a) If z = xy - xei , show that x- ду

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 59. Prove the general formula iwollo oi ons dx 1 x - In x – b + C %3D (x – a)(x – b) a – b - - where…

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Q: Assume x and y are functions of t. Evaluate dx = 9, x = 3, y = 0. for 4xe = 12 - In 729 + 6ln x,…

A: Given query is to find indicated derivative.

Q: 6. Prove that for x > -1 then Vn E N, (1 + x)" >1+ nx .

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Q: If f(x) = exp(-x).In(x), then , when x=1, df/dx is 1/e C 2/e O e nonexistent O

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: tes, sno W inut E [XY] = E[X] E[Y] E [g1(X) g2(X)] = E [g1 (X)] E [g2 (X)1 and

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Q: 73. Use the definition of |x\, the chain rule, and the fact that (In x) = - for x > 0 to prove that…

A: Given, dlnxdx=1x, x>0 from definition of x x=x ,     x>0 -x ,  x<0  if x>0 then d…

Q: y If z = show that = 0. x + y?*

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Q: Prove that m-l dx =0 m +n (し+x)" where m,n are both Positive

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Q: Is it possible to find a number  n  such that is ∫0∞  xn dxconvergent?

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Q: Q6:-Prove that: y" = 1 if y=;csc (tan"

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Q: (e) f(x) = sin(e*) + eco«(a) (f) f(x) = cos(x) In(5x) (x) S(z2) = ()" %3D - 1

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Q: d Prove that (x") = n x"-1 dx

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Q: dy Find Z for y = (8+ x³ In x)ª + e3x

A: We have to find out derivative

Q: S Prove that L(cos 3t) : %3D (s2+9)

A: We know that Lf(t) = ∫0∞e-stf(t) dt Then Lcos 3t = ∫0∞e-st cos 3t dt                             (1)…

Q: Prove that Jn (x) X good dx=1. n

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Q: Use mathematical induction to prove that the n-th derivative of (x +n + 1)e" is given by d" (x+1)e =…

A: We use mathematical induction. The detailed solution is typesetted and given in detailed as the next…

Q: Let f(x, y,2) = x² sin y+y e", where x =t +3,y = ne*-1 and z = In 2t. at t = 1 is: -2 1+2n O -12n…

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Q: az Find for z = x'y'eV

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Q: The evaluation of S V1 + tan2x dx is C In(V2) +1 In(vZ+1) C In(vZ-1) O-In(vZ+1)

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Q: 1. Use the Fundamental Theorem of Calculus to evaluate the following (DO NO 5x -6x dx 1 | cos (x)--…

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Q: Suppose that a) [15x²y; 0<x<y<1 f(x, y) = { 0; otherwise. Compute E(Xy), Var(X) and Var(Y). b)…

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Q: az Find for z = x²y°e®Y dx

A: The given function z is zx,y=x2y2exy We have to find the partial derivative of z with respect to x.

Q: Suppose that a) b) f(x, y) = [15x²y; 0<x<y<1 0; otherwise. Compute E(X | y), Var(X) and Var(Y).…

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Q: ronskian of the DE : xp(x)y' + 3y = 0 = er² et? et?

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Q: Show that E(SSE) = (n - k-1), as in Theorem 7.3f, using the following approach. Show that SSE = y'y…

A: Please find the explanation below. Thank you

Q: If z =e* + In(xy) Evaluate- ,and ,at the point (1, 2). Hence, calculate the change in z when x…

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Q: To prove that 2 dx 2 In V1 + (In x)² + In x| + C X/1+ (In x)² we use the substitutions

A: The given integral is ∫2 dxx1+lnx2 Find your answer below

Q: dy then In z is If y = cosh z

A: Without wasting any time, any further, differentiate the RHS to get your answer.

Q: 9. Let f(x) x In(10) Find the most general antiderivative. F(x)

A: Given data÷ So,we need to find F(x).

Q: Ôz Ôz If Z= tan"'(2) -= 0 show that : *-+ y ôx ôy

A: Let us consider function z=f(x,y) Where f is function of x,y. ∂z∂x represents partial derivative of…

Q: 7. a) Prove that for r > 0 * (E) + c. Vr2 – r²dx = vr² – x² + -1 sin 2 +C.

A: To prove: ∫r2-x2dx=x2r2-x2+r22sin-1xr+C

Q: Prove that x" dx „n+1 + C, n + 1 for n + -1.

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Q: Let X and Y have the joint p. d. f . sx+y if 0<x, y < 1 elsewher f (x, y) = %3D The covariance…

A: Given X and Y have the joint p.d.f. fx,y=x+y  if  0&lt;x,y&lt;1    0          elsewhere

Q: 3. Prove that So 0 1 x + ex -dx = n=1 (−1)n−1(n − 1)! nn

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Q: If x = k (1+ e*) dy _ x² + x°ew/ s° +2yeb/a} prove that dx 2xyely/x}

A: NOTE: Refresh your page if you can't see any equations. . ................(1)

Q: Find Hence evaluate d dr 1 Š S ₁ (1 +2²2)³/26 0 -1 1+x², dx.

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Q: In Evaluate the integral: Sé e x²+3x-7 x-2 dx

A: Option (b) x22+5x+3ln|x-2|+C

Q: If J f(x) cos(mx)dx = and f(x) = En=1 cos(n²z) n3+1 then m = O 4 O 25 O 16 0 4 9 O 5 O2 03

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Q: Find fCx) if flo)=0 and the tanGat (k,F CX) has ine af Slore x(x+2) a

A: Given for the function F(x), F(0)=0 and tangent line to F(x) at x,F(x) has slope xx2+23.

Q: RA Find dx dt x In(x) /1 + (In(x))²

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Q: Verify Young's Theorem z = In(2x + y) y? x2 +e(x+2y) y

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Q: J arctan x dx A C In(x2) + C In(x² + 1) + C x arctanx x arctan X - | 1. x arctan x +- In(x2) + C x…

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Q: Suppose that a) b) f(x, y) = [15x²y; 0<x<y<l 0; 0; otherwise. Compute E(X|y), Var(X) and Var(Y).…

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Q: d'y on of x

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.