Q2 Indeterminate form 0/0 0/2 O

Q: H(x)= In(x+2)

A: our objective is to find x

Q: 4 Find the singular values of [2 2 %3D 1 -

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Q: 3.4 Find the residue of f(2) = (1 – 2º) sin(1/2).

A: Find the residue of f(z)=(1-z^6)sin(1/z) We know that residue of f(z) is the coefficient of (1/z) in…

Q: 10 X =1.2 is to be sol he initial approxima

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Q: 4. Find g[h(x)] if g(x) = x² and h(x) = x + 3. %3D O A. x2-- 3 B. x + 6x +9 O C. x + 3x? O D. z + a…

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Q: (x2 – 1)y" – 2xy' + 2y = 0 - tion ofS the o uation

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Q: meª (In x)-5 Find: What is the behaviour of y as →→ ∞ ? Given: Y- ▬▬▬ Oy -∞ Oy →∞ Onone of the above…

A: Please see the below picture for detailed solution.

Q: 6. lim t+0o e3t + 4t

A: Given: limt→∞t2e3t+4t To determine: The value of the given limit.

Q: 1. Find the roots/s using Secant Method a) x*-x-10 = 0

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: Q.3 а. Using first principle develop a formula of finding AY AX when Y- {(X)+g(X) Z(X)

A: y = (f(x) + g(x)) ÷ z(x)     Hence,  => ΔYΔx  =  dydx  =  ddx(fx+gxzx) By quotient rule of…

Q: 23 + 6x² – 32 1. lim 4 x3 + 5x² + 4x bw e 2. lim w>-00 4+ e 3w sin(6t) 3. lim 40 sin(11t)

A: Given that limit problem and we solve use L'hospital rule . If we apply limit and function is 0/0…

Q: 16. lim x2 cos(2nx) = 0 %3D

A: As per our guidelines we are supposed to answer only one question

Q: 2 8. y' + ²y = -x²y² cos x

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Q: 5. Evaluate the integral. x+7 (x-6)(r-2)*a

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Q: 2x+ Vx* – 3Vx Find the integral | 5/ 2

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Q: Q1 show that fx=|x|sinx and gx=xsinx are independent solutions Q 2 Show that fx=|x| and gx=x ^2 are…

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Q: .(1) t is straightforward to show that y = k-1 is a solution to the homog quation

A: Given,                yk+2 -2k+1kyk+1+ kk-1yk=0         (3.151)and       yk+2 -2k+1kyk+1+…

Q: two iterat x' = -2x+t, using successive approximation. x(0) = 1.

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Q: h 1/27 (5 fn+1 +8fn - fn-1) Xn+1 = Xn + Discuss its local truncation error O(hP+1)

A: “Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: - PROBLEM For any real numbers C1, C2, ..., Cn show that n S COS | CRT₁(x) dx = [] cos CA. k=1 k=1

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Q: 2 Find Ssin xdr In x dr

A: Given and To find the following integration: a ∫3lnxdx b ∫xlnxdx c ∫lnxx3dx d ∫lnx2dx e…

Q: sinh(1+ Inx)= Select one: Zero e?x² – 1 2хе e Inx 2 None e?x²+1 2xe x² +1 O 1+ 2x

A: We need to simplify the following expression sinh1+lnx

Q: du Find a product solution for the PDE x = 0 given u (x, 1) = 14e2* – 7e-3* at

A: a partial differential equation is an equation which imposes relation between the various partial…

Q: (1-3) (x+y) - 4 Find حرقیم CR لا لا للمعاد لك - 031- ans:- X 1

A: You posted multiple questions. As per our policies solving first question.

Q: E-o(-1)"(n+ 1) x“ = (1+x)² 1 2.b) for |x| < 1 %3D n=0

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Q: 6) f(x) =xcos x 2n(-1)" • sin(nx) (n-1)(n+1)

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Q: 1 8. When we say that (Inx) = , we really mean to con- dx 1 on the restricted domain (0, 0). sider…

A: Given the function ln(x) Now for the derivative : ddx(ln x)=1x Here we take the function 1x on the…

Q: 3. f(x) = -x² +1 Ex)(+x). x2 + x - 6 %3D Holes: Vert. Asy: Hor. Asy:

A: Now plotting the graph of given function we get :

Q: Vx+1 * Evaluate | x+ 10 A 2/x+1-9ln|x+10| + C 22 tan-1 V11 x+1 +C B 2/x+1 C none of these 2/x+1 -…

A: Please refer the attached image for complete solution. THANK YOU.

Q: 6 0 8 Find the singular values o1 > 02> 03 of A = -8 0 6

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Q: 3. Derive the reductive formula for S sec" (x) dx.

A: We will find out the required solution.

Q: (9) Lim t-3 sin(z² +4t +3) 1² -9 t'

A: As per bartleby guideline for more than one question asked only first is to be answered please…

Q: · ƒ³3(x + 1)(x + 2)²(x² −1)dx with and without the even-odd theorems (show both solutions).

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Q: =(x1= Find. === 2 × K value X Co oxx cl 1 ≤ x k of

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Q: (2+k)dr Evaluate 1– sec (x+a) 1- sec

A: ∫2+k1-secx+adxTake the constant out=2+k·∫11-secx+adx Now,    ∫11-secx+adxLet…

Q: cos √x+1 O Σ n=2 (-1)"x²" (2n)! n+1 x² Σ nal

A: I have given the answer in the next step. Hope you understand that

Q: p(x) = (e³x+5 + n)³. q(x) = In(5e* + 6 tan x). u(x) = e*In(x)-x+2.

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Q: sin 3y limy0 5y 05 O 3/5 00 03

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Q: 1. Find the constant c that makes g continuous on (-oo, 0). Use the continuity checklist to verify…

A: Solve for c

Q: -t 2 lim 8 cos t 2 T 2 16 16 2.

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Q: x+1 Q1/ Prove that coth-1 x = 2 x-1

A: In this question we need to show coth-1x=12lnx+1x-1.

Q: 5n+7 Find supremum of A :|n E N 4n+12

A: Given set isℝ A = 5n+74n+12 | n∈ℕ We know that a number u is the supremum of a nonempty subset S of…

Q: If  y = tan-1( k x) + tanh-1( k x)  and  (1 - 256 x4 ) = A Then A +k =..........

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Q: 5x Suppose that > Cna". (9 + x) n=0 Find the first few coefficients. Co = C1 = C2 ||

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Q: 6. u (x) = tan(-1) (x*) (-1) (xª) %3D 8. 3t+2 7. k (t) = - () %3D 4t+1

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Q: cosh(1+ Inx)= Select one: e Inx None e?x² - 1 2xe x² +1 O 1+ 2x e?x² +1 2xe Zero

A: We will use definition of Hyperbolic function and properties of Logarithm

Q: 1n 1-Co1 2n

A: To evaluate ∫π4π2 sin 2x1 - cos 2x dx

Q: 19) h(t) = -2t –; Find h %3D

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.