Consider the function f defined on [0, 1] such that f (0) = 1, f(1) = 3,f(1/5) = f(3/5) 4, and f2/5) = f(4/5) composite Trapezoidal rule with 5 subintervals is 1.8, then the value of c is: %3D %3D %3D c. Suppose that the approximation of I = S, f(x)dx by %3D %3D %3D O 0.5 O -0.5 O 4

Q: Consider the function f(x, X2, X3, X4) = x+3XX4+2x2 8xxX4 +3x+7xa? O a. Fis positive definite Ob.…

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Q: Find the decivative of thne function f(xiy)=x²+xy+y? at the point (5,4) Po the direction 3n which…

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Q: find its harmonic conjugateu andd find analytic funchionf(2)=utiV sätisfying the Indicated condition…

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Q: 2. Check the following function f(z) = iz – 3z is analytic or not (Use C.R equations).

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Q: 1. a) Find the local linear approximation of f(x) = x³ - 4x +3 at the point where x = 3 b) Use your…

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Q: Let F(t) = (- t + 1, t – 2t", - 2t). Find the line (L) tangent to r (t) at the point (- 15, – 24, –…

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Q: Find the exact value of F. dr using any method. b. F(x, y, z)= C is the line segment from (1, 0,…

A: The given vector field is Fx, y, z=yz, xz, xy+2z. We have to find ∫CF·dr.

Q: For a functionf: R R, it is known that f(2,3) = 4, f-(2, 3) = -1, and %3D %3D fu(2,3) 1. Then, the…

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Q: The volume V and surface area of a sphere [Figure 6(A)] are expressed in terms of radius r by V(r) =…

A: GivenVolume , V = 11πr3Surface Area , S = 41πr2As V = 11πr3r3 = V11π⇒r = V11π13 = r(V)Now, Surface ,…

Q: (d) Calculate the coefficients (B's) by estimating separately the following models (Use the formulas…

A: The coefficients of β's can be estimated by using the method of least squares.

Q: 0.3, and fy(2,4) 6. Assuming that f(2,4) = 5, f«(2, 4) approximation for f(2.1, 3.8). -0.2, find a…

A: Given that: f(2, 4)=5, fx(2, 4)=0.3 and fy(2, 4)=-0.2

Q: ) Let f(r)= r -92+ 15-7. Find all critical points of f(x). ) Use the second derivative test to…

A: Given function is fx=x3-9x2+15x-7 (a) To find critical points of fx For determining critical points,…

Q: Consider the 2-dimensional function f(x, y) = xy²exp (-³² + y). a) Compute all the stationary points…

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Q: 3. Let w = f(z) = 5z² – 12z + 3 + 2i a. Determine u and v b. Calculate f (3 – 4i)

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Q: If a function of three variables 2, y, z is defined by f(r, y, 2)=-zyz + 4z(y + 2)-3z What is the…

A: According to chain rule of differentiation for a function f(x,y,z) df=dxdfdx+dydfdy+dzdfdz Now if…

Q: The given functions are concave or convex or neither in the domain: 1). f(x, y) = 2r-y-r²+2ry-y² 2).…

A: As per the question we are given two multivariate quadratic equations : f(x,y) = 2x - y - x2 + 2xy…

Q: Consider the three points (2, 4), (4, 6), and (-2,7). (a) Supposed that at (2,4), we know that f₂z =…

A: Let us consider the given function f(x,y) and (a,b) is critical point then fx=fy=0. Determine…

Q: Fit a trigonometric function of the form f(t) = co + c₁ sin(t) + c₂ cos(t) to the data points (0,…

A: The trigonometric function of the form is given by ft=c0+c1sint+c2cost. The trigonometric function…

Q: fi (x) %3D е*, f.(x) %3D хе-* — е-*; [0, 2] |

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Q: Recall the relation between degrees Celsius and degrees Fahrenheit: F = 1.8(C + 32) X and Y are…

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Q: Given the equation y In (x? + y² + 4) = 4, evaluate dy Assume that the equation implicitly defines y…

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Q: f(x, y) = 3x2 +y+ z Find fx at (0,1,1) %3D 1) 0 2) 1 3) 3 4)-1

A: Given: fx,y=3x2+y+z For finding partial derivative of given function with respect to x, we assume y…

Q: Write the Linear Approximation to f(x, y) = x(1 + y)−¹ at (a, b) = (8, 1) in the form f(a+h,b+k)≈…

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Q: 1. Find and sketch the doma in of the function. Ans A f(x,y) =Vy +V64 – x2 – y2 a. ((x,v)| 64 > x? +…

A: Given function is  f(x,y)=y+64-x2-y2 we have to find and sketch the domain.

Q: Find the CDF of the distance of two randomly chosen points of the [0,6] interval. F(x) - if x6.

A: Given x~U(0,6)

Q: Given the following function: R? →R: f (x, y) = x³ + x²y Select the correct statement according to…

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Q: E.g. Let f(x, y) = x² - 2xy + y². The graph and contour diagram of f is given below right. Compute…

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Q: Fit a trigonometric function of the form f(t) = co + c₁ sin(t) + c2 cos(t) to the data points…

A: Detailed explanation:Step 1: Substitute Trigonometric Values into EquationsFor each data point…

Q: dy by definition for the following functions: d.x x +1 Exercises (20.1): Find 1) y = r + 3 2) y x -…

A: dydx of the given functions are solved below in each parts..

Q: Express the given function using unit step function: (t ,0st<4 f (t) = |2 , t2 4 A.) f (t) =t+t u (t…

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Q: 2. Let f C (R) such that f(xo) = f'(xo) = 0 for some ro R. Find the error term associated with the…

A: f∈Cn(R) such that f(x0)=f'(x0)=0 for some x0∈R. The difference scheme is:…

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.