Question (1): Find dx² in terms of t for the following parametric equations: x = 3 + 4 cost; y = 1 - sint

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Q: Solve the given initial value problem. y" + 8y' + 25y=0; y(0)=3, y'(0)=-11

A: Our Aim is to solve the given initial value problem:-y"+8y'+25y=0, y(0)=3 , y'(0)=-11

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A: Given problem:-

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A: To estimate the area under the graph of fx=x+2 over the interval -2, 0 by using eight approximating…

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A: This question is based on substitution of values.

Q: TU The result of f fysinxdxdy = O 1 O -1 O 1.5 O -1.5

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Q: Example For alternative optimal solution Min 3x₁ + x₂ s.t x + 2x2 14 -x₁ + x₂ FI 22 ۱۲/ 2,9x270

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Q: let a = (-1 - 1) and b= (t u v w). define a functionn F: a TO B BY FOLLOWINNG ARROW DIAGRAM

A: let a = (-1 - 1) and b= (t u v w). define a functionn F: a TO B BY FOLLOWINNG ARROW DIAGRAM

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A: Given x+y+z=5, x-y+z=2 2x+y+z=5

Q: Let Z1 = 3 + i and Z2 = 5+2 i. Find 2 Z1 / (Z1-Z2) - (14/5)-2 i O (14/5) + 2i O O O - (14/5) + (2/5)…

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Q: If possible, find the absolute maximum and minimum values of the following function on the set R.…

A: Given function is fx,y=3x2-3y2+1 and region is R=x,y:x2+y2≤1

Q: Q4 Evaluate: f(1- cos²4x) sin4x dx.

A: The given integral is: I=∫1-cos24xsin4xdx   As we know the Power rule. ∫xndx=xn+1n+1+C

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Q: The value of √(-25) is * O -5i O 4i O 5i O-4i

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Q: Question 2.4. Find all cube roots of -1 in the complex plane. 2e ₂ (i) Ⓒ (i) -1 1 e (5₁)

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Q: Q4A) Find area bounded by y = 0, y = √2x-x² using double integration.

A: The required graph is shown.

Q: 1-9 13-9 X x-h 2 3 . sin (lnx²) sinx 2-9 It cosx .dx 4-9 cotx.dx хр

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A: I am attaching image so that you understand each and every step.

Q: * Find dy/dx for the function y=2 sin(3x) cos2x 4 sin (3x) sin (2x) - 3 cos (2x) sin (2x) O 6 cos…

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Q: Express as a single logarithm and, if possible, simplify. log (x²-2x-35) - log (x²-25) log…

A: Using log(a)- log(b)= log(a/b)

Q: Express (+)² in polar form O 3 [cos 67+isin 67] O 13 [cos 70+isin 70] 3 [cos 70+isin 701

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Q: 1. Evalaute lim ƒ(x), lim ƒ(x), lim f(x) for I-3+ H-3- I-3 f(x) = { 2 -x+4 x - 3 x <3 I 23

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Q: Q1/ Find maximum,minimum,and saddle point of the surface Z = x³y³ 12x + 3y + 12.

A: Given :- z=x3 -y3 -12x+3y+12 Find:- Maximum, minimum and saddle point of the given surface

Q: he volume bounded by the function_z = f(x, y) = xy√x² - y² <10 and 0≤ y ≤8. over

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Q: sto

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Q: Consider the function f(x)=2sin(x)+(√3/2) x^2 This function has two inflection numbers A<B in…

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Q: Find the indicated derivative and simplify. [3x log x³] dx [3x log x³] = dx (Type an exact answer.)

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A: According to question,Given data,Material costs = 12 cents/cm2

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A: The given initial-value problem,dxdt=4x2+1, xπ4=1

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Q: dy B)Solve differential equation dx -(sinx+cosy) y²-x siny

A: Exact differential equation

Q: 13. Evaluate the triple integral: In y (z) dzdydx y2

A: Given :∫12∫1x∫y2lnyz dz dy dx=I