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>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....
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- Compute Δy/ Δx for the interval [2,4] where y = 5x−7.Suppose z is implicitly defined as a function of x, y, by means of the equation: z4+8zx=3x2+12y2 The value of the real constant k for the equality: y*(∂z/∂x)−kx*(∂z/∂y) =−2zy/(z3+2x) is true, corresponds to:The line tangent to y = ƒ1x2 at x = 3 is y = 4x - 10 and the line tangent to y = g1x2 at x = 5 is y = 6x - 27. Compute ƒ132, ƒ′132, g152, and g′152
- Suppose a table of values of f(x) = sin(x), 0 ≤ x ≤ 1.58, is to be constructed with the values of sin(x) given with a spacing of h. (a) If linear interpolation is used in this table, how small should h be in order for the interpolation error to be less than 10^-6? (b)If quadratic interpolation is used in this table, how small should h be in order for the interpolation error to be less than 10^-6?If x < 0 and y > 0, determine the sign of the realnumber. xyState why the function 2z2 - 3z + e-z is analytic everywhere.