Find +he obmain ond rage of the hallowing functions 1 i) Cos(x-T) ii) x²+x-2 iii) Lan:

Q: 10. Since (7,-1) is a point on f (x) cos z,which point will be found onf'(x) = cosx ? %3D O a (1,ח)…

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Q: 1 - cos 2x if y = prove 1 + cos x y' = 2tanx.sec²x

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Q: Explain why the function has at least one zero in the given interval.

A: Given function is  fx=x2-2-cosx over interval 0, π.

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

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Q: 5. Show that cos (sin 2x) + sin (cos-1 2x) = (V2-2x)(VZ+2x) -

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Q: Prove that sec x dx = In sec x+ tan x +C.

A: Here the question is solving by using u-subsitution method.

Q: 2) DISCUSS The Contmuyo f Sin TX %3D

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Q: If y=tanx, Prove that Y™ 2 (Y²+1)(3+1)

A: We will find the required.

Q: With mean theorm, show that | cos x - cos y| < ]x – yl for all of x and y at R www.wwwnn

A: Mean Value theorem

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: s nip

A: Given z=tanα2

Q: Differentiate : a. y= x^2 sinx +sin^2x + cos^2x + tan 2x/sin2x/cos2x b. y= In √x^3

A: a) y=x2sinx+sin2x+cos2x+tan2xsin2xcos2xb) y=lnx3

Q: 1- , S" cos(x)esin(x)-8y dydx

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: If f(x) = cos(x) +3z³, what is f'(æ)? O f'(x) = sin(x) +3z³ O f'(x) = sin(x)+ 9x² O f'(x) =…

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Q: Find f'(x). f(x) = O O O 6x - sin² (5x) f'(x) = O f'(x) = f'(x) = f'(x) = = 6-10sin(5x)cos(5x) 2√6x…

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Q: satisfies thé équation:y + 13y - Show that y=e Sin 3x

A: Topic = Derivative

Q: Prove that 1 3V2 dx < 3 + x (Hint: Theorem 5.9(ii) and carefully chosen functions should do the…

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Q: Suppose that 3x² - y² = 1² and y=tsin 0. Find (3). = sin 0 y (1) ¹ (2) and (2) 0 X X

A: Let's find partial derivative of given two equation.

Q: if f(2) = zsin(z) -1 defined on the interval (2. 3] then es using False-Position method equals [x in…

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Q: What is f (=) if f (x) = sin 2x + cos 2x + sec 2x + 8 %3D csc 2x + tan 2x + cot 2x.

A: The given function is fx=sin2x+cos2x +sec2x+csc2x+tan2x+cot2x. To find : the value of function at…

Q: E prove that - Cotx + C %3D 2 |- Cos?x +Sinx

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Q: If Y=tanx prove that %3D2

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Q: Suppose f(x) = π − 2x − cos x. (a) Show that f is strictly decreasing on R. (b) Hence, justify that…

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Q: 8. Show that cos a – cos y| < |x – y| for all æ and y.

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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…

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

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Q: What are the zeros of f(x) = 2 cos (3x) + 1 on the interval [0, π]?

A: The zeroes of a function f(x) are the values for which f(x) becomes zero. We know that, cosx=cosθ if…

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

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Q: Differentiate the function f (x) = 4 cos 3x - 3 sin 4x. %3D O -4sin 3x -3cos 4x O -12(sin 3x + cos…

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Q: 7. B- Show that: (1) lime-0 tan 8 (2) tan 0 sec20 =D1 %3D do

A: Solve

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: A force of F(x)=x2−cos(3x)+2, x is in meters, acts on an object. What is the work required to move…

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Q: у %3DIn(In sec x)

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Q: 4. Ify =/sin x+ /sin x+.to inf inity, dy _ cosx dx 2y-1 prove that

A: Derivative of Sinx is Cosx

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

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

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

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Q: Consider the relation x2z2 = arctan (xyz) + 4, which defines z as an implicit function of x and y,…

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Q: I* cos z lim 1³+2

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Q: If y=tanx , prove that y```=2(y^2+1)(3y^2+1)

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Q: Let w- fx.y.) - :), x- cos(), y sin(» and :. Then:

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Q: Suppose f(x) =cos ( 3x – 2). Evaluate: A -3sin(3x - 2)+C ® -sin(3x- 2) + C sin(3x – 2) +C 3sin( 3x –…

A: Given function f(x) = cos(3x-2)

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: Prove sech 2  x =1 - tanh  2x

A: we have to prove: sech 2  x =1 - tanh  2x

Q: find the area of the shaded 4) reglon y = 2 2- y = 2 sin(Tx) 3 х -1- -2+ -3+

A: From the given graph the shaded part is on the interval x=0.5 to 2.5.  So find the area between the…

Q: Suppose that a particluar funciton f satisfies f" (x) = - (4 sin(x) + cos(x)), f(0) = 3, f'(0) = 5.…

A: f"(x) = -(4sinx +cosx) ,  f(0) = 3 , f'(0) =5 now integrate the f"(x) f'(x) =4cosx -4sinx +c now…

Q: Prove that 2 Sin X dx 1 + cotx + cos x It tan X cos 2 x

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Q: Evaluate f(x) = 7sin r 1 COS -X %3D at a /3. x =

A: Given fx=7sinx-cos12x To evaluate the value of function at x=π3 put this value in fx fx=7sinx-cos12x

Q: Show that:- tan-1 x + tan-1 y = tan-1 x+y 1-ху

A: We need to show the following identity tan-1x + tan-1y = tan-1x+y1-xy