Test for homogeneity  f(x,y)=tanx-sec2x-cosy

Q: Determine the local extrema of the function f(x)=sinx−cosx on [0,2π].

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Q: Find fyyzz if f(x, y, 2) = cos(3y + az). Then evaluate fygazz at point (, 0, 4). COS

A: *Use chain rule

Q: Find the absolute extrema of the function on the closed interval. y = 5ex sin x, [0, π]

A: Solution:-Given functiony=5exsin x in [0,π]∴f(x)=5exsin xf'(x)=ddx5exsin x∴f'(x)=5ex cos x+5ex sin…

Q: sinx xくT。 Discuss The Continuity of y= COSX

A: Continuity :     limx->af(x) = L            where, L is the limit value i.e. finite and will be…

Q: (sinx E,x# 0 a) f(x) = in x = 0 0, x = 0 b) f(x) = x - |x| in x= 0

A: Topic:- Continuity

Q: Differentiate. f(x) = ex sin(x) + cos(x)

A: The answer is found in step-2

Q: Partial Differentiation. If u = In(x² + y²) and z = sin-1 *(÷), evaluat-

A: Differentiate the following

Q: Use Linear Approximation to estimate Aƒ = f(3.02) – f(3) for f(x) = sin(). (Use decimal notation.…

A: Given: fx=sinπx16 We need to estimate ∆f=f3.02-f3 using Linear Approximation.

Q: Integration of (Sin(x) + Cos(x))e^x is_

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Q: Area under the curve x + y = 3 and the coordinate axis

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Q: Sinx Show that gy (x) = conyergos !ナx uni formly to xe Ci,6]

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Q: Prove: sinh(x – y) = sinh(x) cosh(y) – cosh(x) sinh(y)

A: The basic relations we need to know to solve this problem are, sinh(x) = ex- e-x2cosh(x) = ex+ e-x2

Q: tan x + i tanh y 1- i tan x tanh y 18. tan z = tan(x + iy)

A: We have to prove

Q: (secy y It Secx Sinx + tanx sec x t CSCX It tanx tan x y =

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Q: The coefficient of sin'x in the antiderivative of F(x) = cs (use fraction form not decimal

A: This question can be solved using the concept of integration of trigonometric function.

Q: Prove the reduction formula

A: To prove: ∫tankx dx=tank-1xk-1-∫tank-2x dx

Q: sin(x + y) - sin(x- y) 2 cos x sin y

A: Solve the following

Q: X-|x Show that f,given by f(x) = (x ±0) is continiuos on R-{0}

A: f is continuous at a  If at x= a L.H.L = R.H.L = f(a)

Q: f(x)=\arctan (1-x),[0,1]

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Q: 4 Test for homogeneity fx,y)- tanx- see'x - Osy

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Q: of of +y y Let f(x, y) = x$y² tan Then x equals X

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Q: (II) 1 f (x, y, z) = arctan 2 (x + y)²

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Q: Topic: Integral of Hyperbolic Function ∫(sinh(x) + cosh (x))^2

A: Given- ∫sinhx+coshx2dx To find- The value of the integral. Identity Used- The above integral can be…

Q: Using Integration By Parts, x sec - x tan x dx = %3D

A: Use integration by parts.

Q: y = tan In(x + sin x) %3D y = sin x + In sin e* %3D

A: y=tan ln(x+sinx) y=sinx+ln sinex

Q: Test for homogeneity 3. f(x, y) = tanx - sec²x - cosy 4. f(x, y): x²+3xy

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Q: f(x)=sinh(x)+2cosh(x)-sech(x) O f(x)=cosh(x)+2sinh(x)-sech(x)tanh(x) O…

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Q: 25. Integrate sec³ ( }x)dx O sec(블지) tan(금r) + 1lmscc(x X- O sec(금x) tan(금x) + In]sec(3r) ○3 sec(금x)…

A:

Q: Show that

A: Given: verify that secx=sinxcosx+cosx1+sinx for verifying given identity, we solve left hand side…

Q: siny dle = (1-x cosy) Cas y

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Q: d -tan(z) = dz sec(x) O cot(x) O sec2(z) O

A: we have to find ddztanZ i.e we have to find derivative of Tanz with respect to z ddzTanz=sec2zdzdz

Q: II. Derivatives of Transcendental Functions. 6. y = x²e 7. y = 52x+1 8. y = In|sinx| 9. y = xlnx – x…

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Q: Use a computer algebra system to analyze the function over the given interval. f(x) = sin(x) –…

A: To find the derivatives of the function

Q: (x² cosh(sin(x– y)): - »)= (x² cosh(sin(x – ))= v+coshz ôvôz

A: As per the guidelines I could solve only part 8. But as part 9 and 10 are short to answer, We will…

Q: (sec2 0 – sin 0) de sec y (tan y – sec y) dy 1 2

A: Given:- 1. ∫(sec2θ - sinθ)dθ2. ∫secy(tany-secy)dy

Q: Area under the curve y = 4 - x2  from x=-3 to x=3

A: Please see the answer bellow.

Q: differentiation to find in terms of x and y. dx In(y) + 3xy - 4 = x² - 2y 5. Use implicit

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Q: esinh dx sech x

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Q: tanx - tany = sin(x+y)/cosxcosy

A: The given identity to be proved is,

Q: tanx If f (x) = A (В) (ⒸC) D - St 0 sec 3x 1+ e tanx In (secx) √ 1+tan ²x 1+ e tanx sec²x 1+elanx…

A: Finding the derivative of the integral

Q: y = Vsin (x)+ /sin(x)+. sin (x)+ sin (x)+ Vsin (x)+

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Q: Of of Let f(x, y) = x°y² tan y Then x +y. equals

A: The derivative of a function of two or more variables with respect to one variable, while the others…

Q: sin x dydx sin x sin x dA = dzdy = %3D 0.

A: Let's first draw the region of Integration and then evaluate the integration.

Q: sin(ln x) r→0+ In(sin x) Use Squeeze Theorem to evaluate lim

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Q: Integration of (sin(x) + cos(x)) e^x is ______________.

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Q: Secx tant I seex+ Secx+3

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Q: cos y sin x Let f(x.y) x+0 %3D cos y x=0 Is continuous at (0, 0) ?

A: Continuity

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.