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

Q: Examine the differentiability of the function f(x)=|cosx| at z 2 %3D

A: Given: f(x)=|cosx|

Q: 4) Estimate tan (0.5) using the tangent line to y = tan(x) %3D 6

A:

Q: Show that f Va²-t²dt = a² sin-¹(2) + x√a²-x².

A:

Q: Identify and sketch the domain of sin-1 (y – 2x) V1- x f(x,y)

A:

Q: Show that J (x) = 2 sin x

A: By definition,                  . Now,  we need to prove the above statement by taking n = 1/2.

Q: Find the minimum value of ∣sin x + cos x + tan x + cot x + sec x + csc x∣ for real numbers x.

A:

Q: Determine of y = cos(x) – V5a2 In x.

A: I have stated the used formulas in the solution.

Q: On (-∞, ∞), three functions y₁(x) = cos 2x, y2(x) = sin² x, y3(x) = cos²x are linearly independent…

A:

Q: : Prove thati Od tanx= sec>x 2. 3d secx= sec x tan x 2: find first derivative following Bi funCtion…

A: Prove that1. d(tan x)dx=sec2x2. d(cot x)dx=-csc2x3. d(sec x)dx=secx·tanx4. d(csc x)dx=-cotx·cscxSome…

Q: Example: show that u(t)=sin t i + cos t j+ 5k has constant length and is orthogonal to its…

A:

Q: Prove that Va2 + 4 sin ( sec %3D V2 +4

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

Q: Qs:- Prove that fez) = cx-g') + ( are harmonic function of (xy) ,but not hormonic conjugates.

A:

Q: 3G)Ú) Show that the reduction formula for atanx で-u sec"x dx = Sec" 「キu ) Hence use tthe formula to…

A:

Q: tan x 1. Differentiate the function: Y = ea* In x

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Q: Calculate for w-z sin(xy+).

A: The given function is w=zsinxy4+9z

Q: Differentiate the function.   f(x)  = Sin (In x)

A:

Q: 3. Show that the complex function f(z)= cscz =1/ sinz satisfies the Cauchy-Riemann condition. Find…

A: The given function is fz=cscz=1sinz. A function fz=ux,y+ivx,y, satisfies Cauchy Riemann equations…

Q: Assume that y is a differentiable function of r such that y² = x² + 4x sec y. Find y' by implicit…

A: implicit differentiation

Q: Differentiate the function. f(x) = cos(In(4x)) %3D

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Q: 2) Proof that If y = f(x) = = cos x then dx sin x

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Q: 5. Verify whether the function f(z) Cauchy-Riemann equations or not. sinh 4x cos 4y + i cosh 4x sin…

A:

Q: Prove that f (x) = x3 − 12x is differentiable. Compute f'(x) and findan equation of the tangent line…

A: For a function f(x) to be differentiable the limit limh→0f(x+h)-f(x)h must exist. This limit is…

Q: Differentiate the function. f(x) = sin(7 In(x)) %3D f'(x) =

A: Given function :

Q: Show that bothy= sinx and y = cos x satisfy y" = -y

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Sketch the graph of two functions g(x) = cos x and h(x) = on the same plane. Choose [a, b] that…

A: Given g(x)=cosx and h(x)=x/2

Q: Sketch the graph of two functions g(x) = cos x and h(x) : plane. Choose [a, b] that satisfied |b –…

A: Given function is g(x)=cosx and h(x)=x/2

Q: Use the second fundamental theorem calculus along with the chain rule to find sint dt dx sinx 2x…

A: We have to find          ddx∫1xsint dt using the second fundamental theorem calculus along with the…

Q: Differentiate the function. a) f(x) = sin(In x)

A: Derivative.

Q: by using mean value theorem prove |sin(x) – sin(y)I < ]x – y|

A: To prove sinx-siny≤x-y Let f(t)=sint ∀t∈(x,y) Then we have the mean value theorem f'(c)=f(x)-f(y)x-y…

Q: Differentiate the function. f(x) = 5 sin2(x) − 8 cos2(x)

A: Given:

Q: (2x) Sinx 2. Prove that (1) Jy₂ (x)=√√(x) =_ (11) J-y₂(x) = √(3/1²) Cosx

A:

Q: = tanh (2x) Use the definition of the hyperbolic functions to prove the identity 1– cosh?(2x)

A: 1-1cosh22xUse the Hyperbolic identity:  1coshx=sechx=1-sech22xUse the Hyperbolic identity:…

Q: Prove that: sin z = sin x cosh y +j cos x sinh y

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

Q: 1, cosX, cos 2X,--- , cos mx

A:

Q: The derivative of sec² 2x (cos² r - sin² x) with respect to a is O2 sec 2x tan 2x O4 sec² 2x cot 2x…

A: Find the derivative

Q: 5) Use the Fundamental Theorem of Calculus to define of the function fol=sin (x?+!) ant-derivative…

A: According to the fundamental theorem of calculus, the following expression is to be true if F is the…

Q: plot these functions using sub plot : x1=siny cosy , x2=secy siny, x3=sin(y-0.5) cosy , x4=…

A: Graph of function  1

Q: Explain how to use the differentiation part of the Fundamental Theorem of Calculus 2+sin(41) 3-9 to…

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Q: Sketch the domain of the function. f(x, y) - sin 1(x + y) y

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Q: (폭), Let f (x) = x5 sin- Then %3D f'(x) =

A: Given that, fx=x5arcsinx27To find f'(x)

Q: Prove the identities Then use them to show that a. sinh 2x = 2 sinh x cosh x. b. cosh 2x = cosh²x +…

A: Here we have to use the given identities to prove.

Q: 1. Find the point(s) if any where f has a horizontal tangent line. у %3D УЗх + 2 cos x 0<x < 2п

A:

Q: Find at the point (5, -1,5) where z is defined implicitly by the equation y°z + x cos z = z sin x.

A: Differentiate both sides partially with respect to y

Q: 5. Find the slope of the graph of cos(x + y) = 2x at the point ( 0, n/2 ). Hint: Differentiate…

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: (b) Verify that f(x) = 2 cos(x) sin(x). f(x) = sin(7x) + sin(8x) 7x + 7x = 2 sin 2 = 2 sin |co(-)

A: Let the function is  f(x)=sin(7x)+sin(8x)   Formula used: Sin(a)+sin(b)=2sina+b2cosa-b2

Q: Verify that sin(x+y)+sin(x-y)=2sinxcosy

A:

Q: 26. Show that the function has removable discontinuity at the origin sin 2x {²7, 2x 1 f(x) = if x =…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.