1. Suppose f(x) = 2-x and g(x) = x2 a. Find (f ° g)(x) and identify its domain. bi Find (per) and Identify its domain

Q: If k > 1, the graphs of y = sin x and y = ke¯² intersect for x > 0. Find the smallest value of k for…

A: Given that if k≥1, the graphs of y=sinx and y=ke-x intersect for x≥0. When the graphs are tangent,…

Q: Given f(x, y, 2) = 4 sin(x + y), find f,(0, . -3), F,(0, -3), and f-(0, -3). 4 -3 4 40. -) - 4 II II

A: Answer is 0  Explanation is given below..

Q: If sin' 0+y cos e sin e cos e and x sin e = y cos 6, prove that x + y* = 1.

A: Solution

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: Which of the following can be differentiated without using the Chain Rule?  (a) y = tan(7x2 + 2)…

A: Given: (a) y = tan(7x2+2)  (b) y=xx+1 (c) y=x·sec(x)d y=x · sec(x) (e) y=xex(f) y=sinex

Q: Suppose z is a function of x and y. Solve for ∂z/∂y if tan √(y^2 + x^2 + z) = z^(x)e^(6y).

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Q: sin, ifx T 2л

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Q: 2. If f(x, y)=x² cos y-y' sin x-xe'-ye* +2x*y', show that ôxôy ôyôx

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Q: If g(x) + x cos(g(x)) = x^7, find g'(0). g(0) was not given.

A: Consider the handwritten solution. We have given that g(x) + x cosg(x) = x7 ....(1)and we have to…

Q: () -1 -3y If f(x, y) = tan %3D then find fr .

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Q: 2. (a) Let f(x, y) = x² sin(x + y), find 잃 and 잃.

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Q: 1. If y= tan x, prove that y"= 2(y² +1)(3y² +1).

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Q: if g(x)  = x Sin-1(x/4)  +  √(16 - x2) , find g'(2)

A: The product rule is used for the LHSwhere as power rule  for the RHSg(x) = x sin-1x4+16-x2g'(x)…

Q: if y=tan x,prove that y'''=2(1+y²)(3+y²)

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Q: 1. If y= tan x, prove that y``= 2(y² +1)(3y² +1).

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Q: If f cos xdx = A +B sin x + Csin²x+ Dsin³x+ Esin*x+ Fsin5x, what is , 2 ) and ( - 2,5). the value of…

A: Given: ∫cos5xdx=A+Bsinx+Csin2x+Dsin3x+Esin4x+Fsin5x.

Q: If g(x)=cos2x and f(x)=sin (1/2) (π), find g(f(x))

A: Given functions are  g(x)=cos2x and f(x)=sinπ2

Q: Suppose z is a function of x and y. Solve for dz if tan Vy? + x2 + z = z"e6y.

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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: If x, y and z are independent variables and f(x, y, z) = x sin(y + 3z) of then find ôz .

A: Here, x,y,z are independent variables. Given function is f(x,y,z)=xsin(y+3z)

Q: If y = xsin then y is equal to = X" at x =

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Q: Find if f(x, y) = x2 +2xy cos x .

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Q: If F(x,y,z)=sin(x³y²)+cos (Vxy2)+x®y²z, then fyz(1,-2,1)=

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Q: bx + c Given tan 3 - In(x2 - 8x + 25) + 1 -dx %3D x2 - 8x + 25

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Q: In evaluating 2 2 dx XV is same as evaluating lim_ cos-¹(f(x)). Determine the value of f(x) if x=2.9…

A: As per the question we are given a definite integral and we have to find the primitive of the…

Q: Hence, using chain rules find y' i. y = sin(2x² + tan(6x² – x)),hint: u = 2x² + tan(6x² – x) ii.y =…

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Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y (π/8) = 0…

A: Given,y(x) = C1 sin2x + C2 cos2x + 1 — (1)Here we find the value of C1 and C2 such that the equation…

Q: Find F'(x), f"(x) and f'"(x) for f(x)=x$+cos(9x).

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Q: If y = tan x, prove that y``= 2(1+y² )(3+ y²).

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Q: Eliminate B and a from the relation: x = B cos(wt + a)

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Q: 3. Use the Intermediate Value Theorem to show that the following equation has a solution. sec(x) =…

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Q: Suppose, f'(x)= 2 cos x+sec x, -7<x<, and it is known that and it is known that f()=4. Find the…

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Q: If g(x) sin(x) then g'(x) = g'(4) = %3D

A: Given the function g(x) :

Q: 7. Let f(x,y)= a) T 2 xsin y-y, find sin x+y Simplify and give exact value

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Suppose that w = x² + y? + z², x = cos 0, y = sin 0, z = tan 6. Use the chain rule to find dw when 0…

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Q: Given f(x,y,z) = sin (2xy) + 5xyz3. Find fyzy(3,2,4).

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Q: 5. If f(x) = (sinx)² and g(x) = 1+ (cosx)², Then What is the relation between f' (x) and g' (x)?…

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Q: If y= tan x , prove that y`= 2(1+ y² )(3+ y²).

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Q: E. If f(x) = sin x + In x, find f'(x). Check that your answer is reasonable by comparing the graphs…

A: f(x)= sin x+ ln x So, f'(x)= cos x +1/x

Q: If y = (x – a)/2ax – x² + a² sin¬'(÷ prove that y' = 2/2ax – x² a is constant.

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Q: If f(x, y) = x² tan¯' (4) – y² tan¬1 (4) , then fy(0,0) = 1 -2 2 -1

A: Given: f(x,y)=x2tan-1yx-y2tan-1xy To evaluate: fxy(0,0) We know that fx(x,y) is partial derivative…

Q: Let z be a function of x and y implicitly defined by the equation xye" – In (x² + y) = sin(x-z2) i)…

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Q: If y= tan x, prove that y 2(y² +1)(3y² +1).

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Which of the following can be differentiated without using the Chain Rule? (a) y = tan(7x 2 + 2) X…

A: Differentiation: y=tan(7x2+2)dydx=sec2(7x2+2).ddx(7x2+2)dydx=sec2(7x2+2).(14x)dydx=14xsec2(7x2+2)

Q: Suppose the true relationship of Y and X, Z is given by 1. Yi = B1Xi + B2Zi + ei under classical…

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Q: Q6:-Prove that: y" = 1 y =csc(tan"" ) if

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Q: Determine cı and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y () = 0…

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Q: 1. If y= tan x, prove that y= 2(y´ +1)(3y² +1).

A: Use the following differentiations as, ddx(tanx)=sec2(x)ddx(sec(x))=sec(x)tanx Now, differentiating…

Q: Express Q (x) = cos* (x² + 1) as the composition of three functions. That is, identify f, g, and h…

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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....