Given a function f(x,y,z) = (x+10) In (5y - 6) sin (5z). Find the domain of the function.

Q: 2. If f(x, y)=x² sin y-y cos.x-xe - ye" +5x°y°, show that ô²f _ ô²ƒ ôxôy ôyôx

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Q: 1. Given f(x, y) = e sin(x² + y² ), find -2x and ôxôy ôyôx

A: Given: f(x,y)=e-2xsin(x2+y2)

Q: sin, ifx T 2л

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Q: Let a be a constant, Evaluate[ (a* + x² + a) sin(3z") + 15z*)dzr.

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Q: a) f(x) = 3x + 5; interval [1,2]; %3D W = 10 interval ; 11m- b) f(x) = sin x;` %3D W = -1 2' 2

A: To verify the IVT for the specified function f, the interval a, b, and the indicated value w.a…

Q: 17. Derive A) f(x) = 10x* –- 32x + e² %3D B) y = e-* sin x

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Q: c If f" (x) = 18 cos 3x and f' (0) = f(5) = 1, find f(x).

A: The solution of the problem is given in the next step.

Q: Q3.lf f(x,y) = sin²(x-3y)+sin(xy find: and af dy ax

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Q: Given that f(r) = sin z cos2 r + 2 = (sinx + a)² + ³ , the value of the constant and the least value…

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Q: For the function f(x,y)= (x² + y²) tan(ln(xy)) + e(x-y) which of the following is the value of…

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Q: Assume that f(x) is a differentiable and invertible function so that f(3) = 4 and f'(3) = .…

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Q: Given a function f(x,y,z) = (x+7) In (6y - 4) sin (1z). Find the range of the function.

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Q: Given f(x, y, z) = 4 sin(x + y), find f, -3 -3 and f. -3 2

A: f(x,y,z)=4sin(x+y) we simply replace value of x , y and z

Q: Evaluate the integral (Trigonometric Substitution) x*dx (x² + 1)²

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Q: Find and of the implicit equatio: a 3x?z + y – xyz' = 0 b ye-* + z sin x = 0,

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Q: d) f(x) = sin x,-n/2 < x < 5a/6 e) f(x) = sec x, – n/3 < x <n/6 %3D -

A: (d) f'(x)=cos xf'(x)=0⇒cos x=0⇒x=π25π6-π2=5π6-3π6=2π6&gt;0⇒π2∈-π2, 5π6f''(x)=-sin xf''π2=-sin π2=-1…

Q: Given a function f(x,y,z) = (x+4) ln (9y - 2) sin (2z). Find the domain of the function.

A: Let's find.

Q: For f(x, y) = sin(9xy) evaluate fz at the point (2, 4

A: Answer is mentioned below

Q: sin(x³ + y* ) Q3. Find of for the functions: .(x.y) (0,0) x'+y f(x.y) = .(x.y) = (0,0)

A: f(x,y)=sin(x3+y2)x2+y2 uv'=vu'-uv'v2

Q: Given, f (x, y) = sin (x²y – 2x + 4). Find fy. - x cos (x²y – 2x + 4) x² cos (x²y – 2x + 4) O-x² cos…

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Q: Given a function f(x,y,z) = (x+1) In (10y - 6) sin (4z). Find the range of the function.

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Q: Let f(x)= sin(x) – e¯*, po=0, and p,=1, then by Secant method p2=

A: f(x) = sin(x) -e-x  p0 = 0 and p1= 1

Q: Determine the domain of the function f(x) = V 3x + 5 sin(5x).

A: to find the domain

Q: GIVEN: f:0,2x]- -R, f(1) = sinz+ cos I %3D Find f (x) in factored form.

A: Differentiate the function fx with respect to x.

Q: Given a function f(x,y,z) = (x+5) In (4y - 5) sin (10z). Find the domain of the function.

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Q: Find of the function f(x,y) = sin(x²y³). əx3

A: The product rule of differentiation : (PQ)'=PQ'+QP' sinx'=cosxcosx'=-sinxxn'=nxn-1 Use the given…

Q: Express the function f in terms of the unit step function: sin(2t) 0st 2n.

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Q: Q3: Given f (x) = sin(x) cos (2x) and h = 0.5, find (numerically): Sf(x)dx а- b- f()(2)

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Q: 3. If f(x) = cos(x), determine f(125) (-T). V2 (B) 2 (A) 0 (С) 1 (D) –1 1 (E)

A: we will use nth derivative formula of cosx .

Q: 12. V5z-8 f(z) = 13. f(x)=sin(3x² +x)

A: We can answer both the question as below using chain rule.

Q: a fif f" (t) = 2e* +3 sin(t), f(0) =-8, ) =

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Q: For the given function f(x) = cosx, let xo = 0, %3D X1 = 0.5, and x2 = 0.7. Find the value of…

A: From the given x=0.75, x0=0, x1=0.5 and x2=0.7. It is known that, the lagrange interplotation…

Q: Given that f"(x) = cos(x), f'(x/2) = 4 and f(r/2) = 7 find: f' (x) = sinx+3 f(x) =

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Q: a.) If     f(x) dx   = 4x9 − 8x6 + C, find f(x). f(x) =

A: Given: ∫fxdx=4x9-8x6+c                                          ..1 for finding fx, we differentiate…

Q: b) y" + y' = sin 2x

A: here we need to find the particular solution of given differential equation. the solution is…

Q: off f(x) dx, where Evaluate [ f(x) f(x) dx = f(x) = 18x², -T≤x≤0 19 sin(x), 0≤x≤T.

A: We have to solve given Questions.

Q: Apply the chain rule to differentiate the following functions. Show your complete solutions and…

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question. If…

Q: Given f(x, y) = y ln(5x 6y), find f-(x, y) = fy(x, y) =

A: The function is given by fx,y = yln5x-6y To evaluate : The expression of fxx,y and fyx,y.

Q: Suppose that f(x, y) = sin(4x + 6y) is a function of two variables. %3D

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Q: Consider the function f (x) = 3 sin (x) – 2. Find the exact value(s) of C in the interval [0, T|…

A: We have to find value of c.

Q: V1+ 4t2 dt, find F'(x) Jain -3 11. If F(x) = %3D sin a

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Q: ) Find the derivetine of the fnchiog h(x) = I sinhex-7x 4

A: h(x)=74sinh(2x)-7x2Differentiate w.r.t…

Q: The residue of the function sinz is (z+i)3

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Q: a²f Compute , and Je Te дхду f(x, y)= x'y² – sin 2+ xe" əx' əy

A: Explanation and solution is given below....

Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of at x = 1. %3D df-1 - dx

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Q: The function f : XI→ a + b cos x, is defined for 0 sxs 2n. Given that f(0) = 10 and that f (n) = 1 ,…

A: The range of a function is the values that can be obtained from the function by substituting all the…

Q: Evaluate f(x) dx, where 8x', ={ 7 sin(x), 0<x< a. -T < x < 0 f(x) :

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Q: a² f For the function ƒ(x,y), compute Or d0 if x =r cos O and x=r sin 0 .

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Q: Find fur for f(x, y) = 7xe* y° sin (/x - 3x* +1)+9x°e"

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Q: . If f(x, y)=x² cos y-y° sin x- xe" – ye* +2x²y² , show that ôxôy a²ƒ_ ô²ƒ дудх

A: Explanation and solutions is given below....