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

Q: sin z In(sec z) dr

A: Answer and explanation is given below.. For 17 and 18 please repost the questions

Q: dy Use implicit differentiation to find given dr tan(x + 2y) + cos y = x² – y²

A: From the given problem;   tanx+2y+cosy=x2-y2   Now differentiating with respect to x.…

Q: Determine whether the improper conrergent divergent. or It sin (x) 8. x²+1 dx

A:

Q: sec 3x tan² 3x dx

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: Differentiate. y = In Sin x  - 1/2Sin2 x

A:

Q: Prove the formula for the derivative of a) (Inverse of cotangent) b) (Hyperbolic cosecant) y = csch…

A: formula for derivative of both function is following:-

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  d/dx[cosx]=-sinx

A: We will use the definition of the derivative  Here f(x)=cos(x) So,

Q: Prove the hyperbolic identity of sinhxcoshy-coshxsinhy=sinh(x-y)

A:

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

A:

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 4x F(x) = | cos (t) dt.…

A:

Q: find show that Q Coshz =CoshX Cosy+isin hx Siny

A:

Q: Where does sin x have a horizontal tangent line? Where does cos xhave a value of zero? Explain the…

A: Concept: The function f(x) at the point x=a, is a line that just touches the graph of the function…

Q: x + y ди show that x 1 +-sin 2u = 0 4 If u = cot - x +

A:

Q: + Bsin z Differentiate @ wi th xespect to x - - S"d (use dy A sinz + B cose

A: Given that: y=Acosx+Bsinx

Q: Evaluate the definite integral. sec (x) tan (x) dx =

A:

Q: Use Fourier cosine transform to solve y" – y = 3e-4 y' (0) = 0 lim y (x) = 0, as x → o0

A:

Q: Find the derivative. y = sinh 1(tan x) O y = |cos x| O y = 1 /1+tan x O y = 1 Vtan? x-1 O y = |sec…

A: In this we have to find integration and derivative.

Q: tan y-1 . sin y- cos y- 1 www. Prove that tan y +1 sin y + cos y+1 2.

A:

Q: What is the derivative of f(x) =2cos (x)? %3D 2 cos (2x) O -2 cos (2x) O 2 sin (2x) -2 sin (2x)

A: f(x) =2cos2xdifferentiating w.r.t xd(f(x))dx=ddx(2cos2x)

Q: Prove the differentiation formula d/dx [cosh x] = sinh x

A: We use the formula of coshx to find the derivative

Q: COSX TT is analytic about x = Select one:

A: cosxx-π2  is analytic about x=π2

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: (a) Show that tan x = dx sec?x using quotient rule.

A:

Q: H.W using differentiation prove that SinX s Cos, व

A:

Q: Compute the derivative: tan-'(ax) (bx) (a) y = sin='(x²) (b) y = (tan-1 r)³ (c) y = sin

A: (a)   Differentiate the given equation with respect to x, dydx=ddxsin-1x2=11-x22ddxx2=2x1-x4

Q: :Show that the function 1 x sin When x + 0 S(x) =- 0, is continuous but not differentiable at x = 0.…

A:

Q: ind y' by direct differentiation (with respect to x).  y = 99cos(x) and    y = 7x sec(x)

A:

Q: If f(x)=tan x, then show that f(x+y)-f(x) = sec^2x tany/ 1-tanxtany

A: The detailed solution is given below Thank you

Q: the equation of the tangent line to the graph of f(x) = 9 sin(x) + 4 cos(x) at x = in the form y =…

A:

Q: Consider sin °x cos2x dx. f we let 4=cos x, the integrand can be transformed to

A:

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

A:

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: Calculate the integral (sec(x)+ tan(x))² dx.

A:

Q: 13) Use implicit differentiation to show that (tan x) = x+1 1 %3D dx

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: O IT 3 tan'z sec z dx

A:

Q: 3 sec x tan xdx

A: ∫π4π3secx tanx dx

Q: Prove that sinh z = sinh x cos y +i cosh r sin y.

A: To prove, sinh z = sinh x * cos y + i cosh x * sin y

Q: Sin T x13 Discuss The Continuity of y=

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

Q: Evaluate the integral. "1/3 tan (x) sec*(x) dx

A:

Q: Differentiate each of the f cosh(x)+1 cos(r)+1 a. Y =

A:

Q: f(x) = x in the %3D sin 2x + ...

A:

Q: Prove the identity.   sinh(x+y) = sinh x cosh y + cosh x sinh y

A: To show that sinhx+y=sinhx coshy+coshx sinhy

Q: Q4) Prove that dx 1+ 2 sinx || In √3 Χ tan tan x + 2 -√√3 +2 + √√3

A: