prove thatn f(x)=In(cosx), then f1(x)=-tanx

Q: Prove that the equation sinx = 0.3 has at least one solution in the interval (o, ~).

A: Given:sinx=0.3

Q: Q1/ Show that 3(sinx-cosx)*+6(sinx + cosx)²+4 (sinºx+cos°x) = 13

A: Note: We are entitled to solve only one question at a time. To Show:…

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

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Q: Where is the function f(x) is continuous, such that f (x) : In(1-2x)+sin (x 4x+3 %3D [-1, ] – (-) O…

A: We know, ln(x) is defined for x>0. sin-1(x) is defined for x∈-1, 1. f(x)g(x) is defined if…

Q: Show that the function f (x) is continuous on Sin x, r 4 -

A: You have to find the left and right hand limit for the given function.

Q: 7. Show that sin E + x) = G+x): = -cosx.

A: Introduction :

Q: 5) Evaluate the integral: tan 3 x dx

A: Given integral, ∫tan3x dx

Q: Evaluate the integral f sin²(3x) cos (3x) dx.

A: The given integral is ∫sin23xcos53xdx. We have to evaluate the given integral.

Q: Prove that  d/dx[cosx]=-sinx

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

Q: Determine the order of the zero at the origin of f(x) = ² (cos(z) - 1 + sin² (2))

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Q: d Prove that (sin-l x) : dx V1 – x²

A: To show that:ddx(sin-1x)=11-x2

Q: 29.Verify that W[xλ cos(μ ln x), xλ sin(μ ln x)] = μx2λ − 1.

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Q: In(cos ax) ? limx-0 In(cos bx)

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0, ƒ (x) has a root in [o,]. If we…

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Q: Prove that d/dx tan(x) = sec^2(x).

A:

Q: Determine a root of f(x) = 2* +3 cos(x²)-2 with 10-3 accuracy.

A: Given :f(x)=2x+3cosx2-2

Q: Prove using the IVT. tan-1x = cos-1x has a solution.

A: Given :                      tan-1 x = cos-1 xSolve :                     tan-1 x = cos-1 x…

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (²-) < 0, ƒ (x) has a root in [0]. If we…

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Q: d Prove that sin x cos x from first %3D dx principles only. Be sure to prove any limits that are…

A: Let's learn first principle of derivative because we have to find derivative of sinx using first…

Q: E prove that = - Cotx + C %3D 1- Cosx +Sin'x

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Q: (b) Prove that : - 1) (coshx)² – (sinhx)² = 1

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Q: Prove that sinh−1(x) = In( x+Vx2 +1)

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Q: 31. Verify the formulas sinh-x = In |x + Vx² + 1| coshx = In |x +Vx² – 1| (for x > 1)

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Q: (A) Prove that: cosh x + sinh x = e*

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Q: Let S(x) 9 sin x + 9 cos x "(x) 3= r(-)-

A: A function is given as fx=9sinx+9cosx. The objective is to find the first derivative f'x of the…

Q: If f(x) = 2 tan '(5 sin(3r)), f'(x)-

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Q: 1 If f(x) = 8 tan¯¹(8 sin(2x)), f'(x) =

A: Differentiate

Q: 4. Prove that cos(sin¬1 x) = /1 – x².

A: cos(sin-1x)=1-x2⇒sin-1x=cos-1(1-x2)Let y=sin-1x                               (1) ⇒siny=x…

Q: f cos² x dx

A:

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

A: Given:

Q: Prove that f(x)= sin(5x) < 5x on [0,x]

A: Take the help of derivative and try to prove the given statement in two cases.

Q: provethat 2. 1- cosx +Sin'x

A:

Q: HW/ Prove that: (1) 1-tanif x sechx

A:

Q: Prove that : 1. Sinh'x= In(x+x² +1)

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: x sin 2x sin COSX 8. Prove that: %3D 2x-7

A:

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

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

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Q: Find (algebraically) the absolute maximum and minimum values of f(x) = cos² x+ sin 2x on [0, 5), if…

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Q: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

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Q: Use the Fundamental Theorem of Calculus to find the derivative of h(x)= (from -4 to sin of…

A: This is a calculus problem

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

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

Q: when

A:

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: Show that, for real values of x, 3 sin x f(x) 2 + cos x cannot have a value greater than 3 or a…

A: To show that the minimum and maximum value of the function is -√3 and √3

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0, ƒ (x) has a root in [o,]. If we…

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Q: Differentiate the following functions 4 1-cos2x Y = by chain rule. 1+cos2x

A: To differentiate the given function.

Q: Differentiate with respect to the independent variable. f(x)= (e^x + cos x)^6 (3x^4 - sin x)^2

A:

Q: Prove that for all x € [1, 00), – sinh (- |cosh'(x)|) = V -1. %3D Ouest!

A: Proving of function  sinh(cos-1(x))

Q: Show that 1 − cos x = x2/2 with an error less than 0.003 for |x| &lt; 1/2.

A: Given: 1-cos x =x22;    |error|&lt;0.003Formula:  The…

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

A: