Q1: If f(s, t) = s2t + In(t2- s) find the value of (f sst) a-

Q: Q4 If f (x, y) = x sin y + ey asf ax2ay3 Find

A: Let's find.

Q: Find the antiderivative F(x) of f(x)=x/3(12x2-6), given F(1)=5

A: An anti derivative of a function f is a differentiable function, whose derivative should be equal to…

Q: You have 3 attempts remaining. 20 11 f(x) dz – -| f(z) dz: f(z) da %3D where a = and b =

A: We have to find values of a and b : Concept:

Q: 3) Let f(x) represent the path of a particle. x* 1 f(x) =+ x 2 1 16 2x2 Suppose the particle starts…

A: The arc length = the distance covered along the curved path f(x).  A = the arc length  A =…

Q: What is t' (x) if t(x) = ? ez

A:

Q: Calculate M6 for f(x) = v7x over [3,6]. (Use decimal notation. Give your answer to two decimal…

A: The function is fx=7x over 3, 6. The number of sub-intervals is n = 6. Obtain the step-size as…

Q: dy Find for the following by using appropriate rules: iv. x² + y3 + (lnx)e♥ = 4. y = Vx(3x2 – 1) V.

A:

Q: c. Use antidifferentiation to find f (x).

A: Since, we have asked for solving part-(c) only.Since here it is given that f'(x)=x2 ln x -(i)Here…

Q: d) Let y= Acos2t where A is a constant. Find the value of A such that d y --3y = 9cos2t for all…

A: Given  The equation is  y= A cos(2t) , where  A  is constant  and condition is  d2ydt2-3y=9cos(2t) .

Q: Find the convolution f (t ) *g(t) f(t)=t^2,g(t)=cost

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Q: F F) s an antiderivative of x-+x-, then what is the value of F(1)-F(-1)2 -1

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Q: 2z et f(æ) = 4(). Which is equal to f(1)? %3D Select the correct answer below:

A: Given:fx=4132xf1=?

Q: • 3x² Given that F(x) = | V4 + e' dt, what is F' (x)? (Do not include "F'(x) =" in your answer.)

A:

Q: Q2/ A/ Find the and ar * iff (x.y) = x - xy, x=r² +s and y =r-s as

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Q: Find F(s). F(s) = £{t(et + e5t)2}

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Q: Q5: Find for the following functions: dx (1) In(x - y) = xy + y³;

A: We have to find the dydx of the given function.

Q: *z + yz? + 2ry? - = 0 ve z = f (x, y) ise =? what is the f(0,1) at

A:

Q: Q3) If f(x, y") = x + y? + Vãy find: af(x²y) and Ty) ду afxy)

A:

Q: Q15: Consider the D.E. (x – 1)³x²y" – 2(x – 1)xy' – 3y = 0. Is xo = 1 an ordinary point? Explain…

A: To solve the following diffrential equations

Q: 3x2 Given that F(x) = In t dt, what is F'(x)? 3x 4 + t2 ||

A: Given, Fx = ∫3x3x2lnt4+t2dt  We have to find F'x.

Q: Differentiate the function. y = In(16 + t – P) %3D y' = 1– 3r² 372 6 +t-t -- 6 + t- r 2 6+t-t

A:

Q: (e) For wi at numbers x, - 2SXS 2n, does f(x) = 4? Where does f(x) = -4? f(X) = 4 for x =

A: The given function is: f(x) = 4sin(x) In the interval -2π≤x≤2π

Q: The r.m.s. value of f(t) V2x – 1 across [-2,1] is Answer:

A:

Q: + The f(x) = Vx – 2 defined at (-0,2] T F

A: Given: fx=x-2 A real valued function is said to be defined in an interval I, if fx∈ℝ, ∀x∈I. Now if…

Q: F(X)=x" 2ny dorsn't this haveoninfiection. paint 20here f"(x)=0?

A: By taking derivatives, f(x) = x4   ----> f '(x) = 4x3

Q: Q2: Find ôf ôf - for the function f(x, y, z) = x²y+ y° + xz² and Əx 'dy

A: We will find out the required values.

Q: %3D 3. If GH = 7x + 18 and JK = 81, find x. H G 丰 K 廿 世

A:

Q: Q2: Let f(x) = 2x e-,x> 0 and Let Y = X2.Find G(y)and g(y). %3D

A: Implicit functions are the functions are not directly expressed, these are always expressed in terms…

Q: you know f(t) = L¯'{F(s)}, how would you find {F(s)/s²j? %3D

A: Inverse Laplace transform

Q: (c) Will it always be true that W C X f(W) S (X)?

A:

Q: 1.f AXYZ - ARST, find RS. 40 3x +2 Sx -3 T. 60

A: Triangle Question

Q: d²y Given that x +y³ = 2, prove that dx2 4.

A: Given: x3+y3=2   As we know that; The Power rule: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2

Q: Consider the function f(r) 10r 10 + 9x° 2x2 6. Enter an antiderivative of f(x). Do not enter +c as…

A: Solve for the antiderivative

Q: Assignment: 8 f(x) | Vīdx

A:

Q: Q2: * Q2: y" + ay' + by = f(t) Find a,b and f(t) so that Ypı = et +t? – 1, Yp2 = e2t + t? – 1 %3!

A: Giventhat:¯y+ay'+by=ftand yp1=et+t2-1 and yp2=e2t+t2-1To find:¯a,b and ft

Q: Find f(t). 5s - 1 s²(s+ 1)- f(t) =

A: A detailed solution is given below.

Q: Let z=xln(x2+y2-e4)-3xy, x=tes, y=est. If the value of 2 when s=2 and t=1 is equal to Ae2+Be4, then…

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Q: Find the value of n in the function w = x •rn satisfies the equation Wxx + Wyy = 0, where r2 = x² +…

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Q: then f(0) If F(s) = L{ƒ(t)} where F(s)= &+25+2)(s² ++2s+5) BIKS 2s2 +2s+3 2905

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Q: If you know f(t) = L-'{F(s)}, how would you fine L-{F(8)/s² j?

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Q: rsin 28x /ī+ t² dt and If f (x) = So g (y) = ' f (x) dæ., what is g" (6s )? 168

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Q: If you know f(t) = L-'{F(s)}, how would you find L-{F(s)/s² }?

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Q: Evaluate F· dī where C F = = , and C is given by - T(t) = , 0 < t < T 0 <t<

A: Given

Q: 10 Q5/ Evaluate x*dx ,n 5, using trapezoidal rule.

A: The trapezoidal rule formula is: ∫abf(x)dx≈∆x2f(x0+2f(x1)+2fx2+...+2fn-1(x)+f(xn))...(1) where,…

Q: 0If z-x"f), show that xZ+JZy=mZ.

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Q: The antiderivative of the function f(x) = 4 + 10x is + 5.0x? + c 4 5.0r? +c 4 + 20.0z? + c + 5.0z?…

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Q: ind the antiderivative, G(t), of the function g(t) = (2n²t? – t*)v2n² – t2.

A: