1 d. p(0) [Note that p(0) : к (0)

Q: by first- shifting find L(t2 e-3«) = %3D (s+3): ; * 0 a O (s+3) 2 * b O 3.cO (s+3) 3 1

A: Solution:- Correct option :- a Detailed explanation

Q: The ODE ty" – 3ty' + 3y = t* has a particular solution Yp(t)

A:

Q: 2 (ii) using Convolution theorem. (s+2)(s²+9)

A:

Q: 2. 9y" – 12y' + 4y = e-3x

A: According to our policy at Bartleby, I can solve only 1st question. Given a non-homogenous second…

Q: 5. (5 – x)² * 6 Show that if y=3-x then %3D 6. . (x-s) _ xp 1. dx. 3 Hence, find the value of , 2(5…

A: In differentiation use quotient rule In integration use substitution

Q: The number of defects on the front side (X) of a wooden panel and the number of defects  on the rear…

A: Here, fXY (x, y) = c(x+y) Joint Distribution of X and Y can be formulated as: X\Y 1 2 3 Total of…

Q: 4.2 Apply the appropriate method to calculate the following: 1 = f***-8 I = S x2-4

A:

Q: Question 3 Let y = V9n2 + 4 = (9r + 4)/. Employ the Chain Rule to find y'. -(9x² + 4)¯# · px

A:

Q: 4. Ifu = f(x), then : dx = J x* + 2x² + 1 k + C for some constant k. x² + 1 Compute kf (1). (a) ¼…

A: The given integral is ∫xx4+2x2+1dx=∫xx2+12dx To compute kf1

Q: -n+1 Xn 4 Xn = A Lyn -1 6 . Pn+1 –1 by using the method of elimination. II

A: Given:- xn+1yn+1=Axnyn=24-16xnyn

Q: 3.Eliminate the arbitrary constant on the given equation: xsiny – x²y-3 = C

A: In this question we have to eliminate the arbitrary constant on the given equation.

Q: In +1- 2 dt, if we let V Vt+1-2, then dt is equal to t+1– 2, then dt is equal to A) None 4x³dx ©…

A:

Q: 1. Find the following. Iy(-1, –1) if g(x, y) = x³ – xy² + 3

A: Given g(x,y)=x3-xy2+3 Differentiating g partially with respect to y, gyx,y=∂g∂y=0-x(2y)+0…

Q: the particular solution of the following nonhomogeneous D.E y''-2y'+y=4x^2+e^x     by undetermined…

A: Solve ( d^2 y(x))/( dx^2) - 2 ( dy(x))/( dx) + y(x) = e^x + 4 x^2: The general solution will be the…

Q: d 1) Find sec dt 2)

A:

Q: In t+1-2 dt, if we let t+1-2, then dt is equal to A 2(x2+2)dx (в 4x³dx O 4x(x2+2)dx D None E…

A: Option C is correct.

Q: If z + In(e3* - e + e²) = 0 dz find at the point (0, 0) -3 -2 3. 2.

A:

Q: 32 Q3: If f(z) Find the residues at all the poles of f(z) !! (Z+2)2(Z2-1)

A:

Q: Part (b) 7s +4 Find L-{F(s)} (s + 4)° Let F (s) = s2 + 4

A:

Q: y' +y = diferansiyel denkleminin çözümü nedir? 3 x +- x4 040 + x + x4 x2 + c + x4

A: Option (e) is correct.

Q: 1. Evaluate these: 1 -x* +c dx *dx (i) x'd< (Ans. x² +c J; (iii) |xdx dx (Ans. ); (ii) (Ans. 2 5 );…

A:

Q: 12. Solve the problem: Utt = c*upx + Ax, 0 0, A= constant, и (х,0) — 0, и (0, t) — 0, Ut (x, 0) =…

A:

Q: kx 4+x² If k > 1, evaluate O ka -In|x² + 4 +C 2 Okx -arctan (2x) + C 2 Ok In(x² + 4) + C O arctan…

A: Given: I=∫kx4+x2dx   ...1   As we know the common integral. ∫1ax+bdx=1alnax+b+C

Q: Use the theorem of Leibniz in the following problems: If y=x³e2x find y(m) and hence y(3). julm) =…

A: Leibniz rule states that (f(x)⋅g(x))n=∑r=0n Cr nf(n−r)(x)⋅gr(x) Let fx=e2x and gx=x3

Q: 2. The value of ₁-² dx = ..., for each Chebyshev polynomial Tn (x), n ≥ 0. 1) 플 b) c) 0 d) None of…

A:

Q: Find y' for each of the following. e2a+3y = x2 - In (ay³) %3D i.

A:

Q: 1. Rewrite c(x) x² +5x+2 in the form y = p(x) + r(x) where r has degree less than b. x-3 6(x) 2.…

A: The objective of the question is rewrite the given equation and end behavior.

Q: I(x) = /, (In(t))² e-(t-1)* dt - 3x

A:

Q: 4.1.5. Let f(x,y) = (x² – y², 2xy). Show that Df(a,b) (h, k) = (2ah– 2bk, 2bh+ 2ak) for all (a, b) e…

A:

Q: d [e'- In (21+1)]dt, find g(x) . dx -2 A ex-In(2x+1) 2 B ex_ (2x + 1)2 4 C (2x + 1)² 4 D (2x + 1)²…

A:

Q: d dt |4e-2t 8t x(0)= 1; y(0)=1 alınacaktır. 2418111408 92001 x(1)=? 9200100503 - 241811140 92001…

A:

Q: Show that r n2n-1 r=0

A: Want to  prove:    ∑r=0n rnr=n2n-1

Q: 3X 7- (0²1)y=K²" yp-e (4X-3} 8-(0-20+4)y=x+3x-5x+2 yp=Dx yo= 3.2 -2K 2. to-(D²+2}y=x²+xre+cos3X éte…

A:

Q: 13. Inx /A 1 + K в 1 B x3 + K 3 ei +K D 2 am +k

A:

Q: az dz 10. Compute and for the following equation. dy ,3 eY + xz2 6xy*z³ %D

A: The given equation is: ezy+xz2=6xy4z3...(1)

Q: Example 10.17. Apply Runge-Kutta method to find approximate value of y for x = 0.2 in steps of 0.1,.…

A: Probem is solved using runge kutta method.

Q: 2 In x 1 e* 2 1 In 2x -1

A:

Q: 1. If the pdf is 2x-2/K e^8x-4x^2 , 0 < x < 1 Find K.

A: 1. The pdf is given by  We know that,

Q: L %3D e2t e-3s-6 (s+2)? O e6-3s ( 1 3 + S+2 (s+2)2 O e-3s (s+2)2 1 3 s+2 O e2-3* ( +) 1 (s+2)2 s+2 O…

A:

Q: The fourth term in the expansion (2r + y)' is

A: The equation for the combinations n taken r at a time is equal to Crn=n!n-r!r!.  The continued…

Q: Theorem 8.3.3 If X ~ t(k), then E(X2r + 1) = 0 and µz, = k"- (2r – 1)(2r – 3) ... .1_ (k– 2)(k – 4).…

A: Answer: For the given theorem, The proof is:

Q: はギ Z-X FIMD fyx At (-41)

A:

Q: S f(x) = x² – 2x + 6 x > 1 x4 + 2.x3 + 2 x <1 Show that there c E (-2,3) such that f(c) = 4. (Don't…

A: topic - continuity and limits

Q: -3z2-3 Let C: |z – il = 4 and I = f. dz. Then z²-1

A: Use Cauchy Residue theorem to evaluate this integral.

Q: 5. Let a > 0, find the "generalized solution" to a" + 3x' + 2x = 8(t – a) with x(0) = 1 and æ'(0) =…

A:

Q: 9. 3cos(@t – a), where w and a are constants.

A:

Q: b) Find L[e* S (-os22) dt] and -1 4s+5 * ls-1) (s+2).

A: Laplace transferom and inverse Laplace transferom, using all the properties.

Q: (3) 1. Solve the IVP u +u"=e*-7 tx with y(0)=1, y'(0)=0, y"(0)=1 (where t is a real constant)

A:

Q: -15 ス=スーカー3;w>え崎-k md 。 d o えしデx2) ) 1パx悩)1,) (穴応)し花っ2) - %3D A. 一

A:

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.