Evaluate S.(x +29)ds, where C is represented by F(t) = (2t, -t2, 0 st<2

Q: + The Range of y [2x + 1] is Z. %3D TO FO

A: We can use the concept of function In order to solve the given problem.

Q: Q2) f(x,y) = 2xy x(s,t) = 3s-2t and y(s, t) = s²+4t. Find Je Je as at

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Q: Use the convolution theorem to find f (t) 14 l(s+2)(s-5))

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

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Q: x~e^. ofY=3x+2 and Z= X/4 Find the distratoution

A: Solution

Q: So, which of the following is the solution functiony(t) ? a) y(t)= sinh2t = e* %3D b) y(t) = sin2t –…

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Q: If f(x,y)=xe/2+118x?y, then asf at (1,1) is equal to əx²əy³

A: Given function is: f(x,y)=xey22+118x2y3 Derivative of function with respect to 'x'…

Q: Q4/ B/ If Ø = (x³y²z) and A = 2xz i - 3y²j+ 3xy²k Find 0(ФА) ay əx the point (2, -1, 3)? at

A: Given: ∅=x3y2z and A→=2xzi→-3y2j→+3xy2k→  To find: ∂∅A∂y∂xat the point 2, -1, 3 To solve the problem…

Q: Show that the function f(t) = 1² – } is a solution of the dif- ferential equation (y')² – 4y = 2.

A: Given:       f(t)=t2−12.Differential equation is: (y')2−4y=2

Q: f(x,y)=ylnxsinx, find fxxxxxy(π,1). Keep your answer to 3 significant digits.

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Q: f(x,y)=xe*/2+275x²y³, then at (1,1) is equal to əx²əy³

A:

Q: dy If y = V2-x, then find de 10. A 2-x 1 В 2/2-x 1 C 2-x 1 D 1.

A: Given y = 2-x we have to find dydx.

Q: IF f(x,y) = y³e-5x find fryy at (0,1)

A: We need to find the partial derivative fxyy of f(x, y) = y3e-5x at (0, 1). Let us first find fxyy.…

Q: Given f(x, y) = 12/8x* + 6y + 2xy°, find f. (x, y) = f,(x, y) =

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Q: For T: R5→R3 and nullity(T) = 2, find rank(T).

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Q: y = 2sinx and y = 0 from x = T to x = 4 π 2

A: The given curves are y=2sinx and y=0 from x=-π4 to x=π2. So, the bounded region is as shown below;…

Q: (x.yız) (x,9e)x4か t. 22 P( 3-1,0) けこくりん)2

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Q: IF Y= 2x² + 5x dy and d = 4, find at when x = 3.

A: See this solution in below

Q: Suppose z is a function of x and y, and csc Vx2 + yz = 2"esin . Solve for dz and ду

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Q: Find dy for the given values of x and ∆x. ; y = 2x3 + x2 - 4x; x = 2, ∆x = -0.2

A: Find dy for the given values of x and ∆x.

Q: 3. If GH = 7x + 18 and JK = 81, find x. %3D H G 丰 K %23 世

A: In this question given that two triangles and both are same . Their sides are same and we can say…

Q: 20.t2y′′+3ty′+y=0,t&gt;0;y1(t)=t−1

A:

Q: Q3) If y² + xy = 1, find y" at the point (0, -1)

A: We will differentiate twice and find the value of y" and it will be equal to,   - 1/4      The…

Q: Given f(x, y) = 4x³y², evaluate f(1,y) and fy(x,2).

A: We are given a function: f(x,y) = 4 x3y2 We need to find the partial derivative of the given…

Q: dz Suppose z is a function of z and y, and csc Vr² + yz = 2ªešinz. Solve for dz nd ду

A: Derivate partially wrt x and y respectively

Q: 3 S(x) = 6x² + x – 7 Find the coordinates of the point of inflection on and prove that it is a point…

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Q: If f(r, y) = (3r" + 21 – 12)', then fy is given by : %3D

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Q: If f(x, y) = (2x? + 8y²)í, then f_(0, 0) = %3D A) 0 В) 1 C) 4 D) 2 E) Does not exist

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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 x E R that satisfies -2 , – 02 + 2 vz U2 det = x det + – ö4 2 0 + 03 U3

A: The key concept to solve the given problem is that : The determinant of a matrix remains unchanged…

Q: Given f(x, y) = In Vay³. What is the value of fy (1, 2)? If the answer is a fraction, write your…

A: Given:  fx, y=lnx2y3 To Find:  To determine the value of fy1, 2.

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: Given f(x, y) = 9xy® – 6x*y. Compute: a?f ду? ||

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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: Given that (r²- (x² – 4)? y = x>2 show that Ax² + 12 dy x>2 dr x*(r² - 4)? where A is a a constant…

A: From property of derivatives,

Q: If y = u³ - 2u + 1, where u = 2√x, find at x = 4 -23 23 33 none of the above dy when x =

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Q: Find for following ds 1.y = (x³ + v3x)S

A: As per our guidelines we are supposed to answer only first question. If you want solution of another…

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

A: Given

Q: Find a - b - c; for b>0. Given PS: f(x) = [n! (2x + 1)"] with : n=0 ROC: R = a IOC: (18 C

A: The give power series is                            f(x)=∑n=0∞n!2x+1n  with:…

Q: dz Find from the equation x*y+ x z+ z² = 4 ax

A: We differentiate both sides with respect to x, considering z is a function of x.

Q: for the -j 3 O de terminant 2-j3 3 2 i-s 1

A: det3j2-3j3-3j-120-j1-j=3jdet-12-j1-j-2-3jdet-3j201-j+3·det-3j-10-j=3j-1+3j-2-3j-3-3j+3-3=-3-6j

Q: Find f, and f, for f(x, y) = 11(2x – 6y + 5)*. fx (x.y) =D

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Q: Determine dz for z = f(x, y) = e^(x2y2) if x changes from 1 to 0.99 and y changes from 2 to 2.02.

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Q: If x) is shown below 3 Then y(t) x(3t – 3) – 1 has the shape

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: For f(x, y) = ln(2x+16)/(2y+16) , find the domain.

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Q: Find d²y/dx2 for the followi f) x2/3 + y2/3 = 1 %3D ³ g) x + y = 16

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Q: Find dy for the given values of x and Δx. y = 6x3 - 7x ; x = -3 and Δx = 0.3 .

A:

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.