Let f(x) = w when 0 < x < a and 0 otherw 00 w sin ak cos()dk =

Q: Let ro)-플-x a-글 FW) = b = 0, and n=3. Then: cos (f(x))dx =

A: We can find the integration as below

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

A:

Q: (a) Find dy/dx for 3 tan x – In x x2 (b) Find f"(x) for the following function: e" In(x**) f(x) = x…

A:

Q: -Vx+ 1+ In(x) e* lim + sin (x)cos(x)

A: Find the limit

Q: Find the extrema of f(x) = 2 sin x − cos 2x on the interval [0, 2 ].

A:

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

A: To show that:ddx(sin-1x)=11-x2

Q: Q1) Show that: (b) (cosx) = -sinx =1+* (a) (1+x) =1+6x %3! (e) (VF) = (d) v1+ tan x

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find f(x) given that: f'(x) = 2 cos x -3 sin x and f (주) %3D %3D

A:

Q: prove that f(x) = sin*x + cos*x is a periodic function with periods

A: We use the Given Equations Prove that f(x) is a periodic function with period pie/2.

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

A: The given function is w=zsinxy4+9z

Q: 2. If f"(x) = 4 sin x +16 cos x, f(0) = 6, f'(0) = 1, find f(x) and f ().

A:

Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

A:

Q: If the function = (x)S x' +1 cos( 2 7x - a) if x < -1 is continuous at if x 2 - 1 x = -1 , find the…

A: Given: fx=cos2πx-aifx&lt;-1……1x3+1ifx≥-1……2   To find: Value of a where fx is continuous at x=-1.

Q: If we have to check the DE sin(x). dy +y cos(x) = 1 dx for Exact then My = - sin(x) -sin(x) -cos(x)…

A:

Q: dy Find f(x)3D3 cos x cotx

A: Given, fx = 3 cosx cotx   We have to find dydx

Q: Determine the concavity of the function f(x) = cos x^2 + sin x^2 + x^2 between x = -1.5 and x = -2.5

A:

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: 1. Calculate the Integral sin x cos x dx

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

Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1. .......Integrate f over the given interval of x, using…

A: Solution:

Q: The f xcos x² 1-sin x2 dx is

A: Given :

Q: If f(x) = (A) B - St √1+1² 1+e' 0 In (secx) √ 1+tan²x tanx 1+e 1+tan²x tanx D tanx 1+e sec ³x 1+…

A:

Q: Show that sin x dx=1-cos t (0<x<t<}r).

A:

Q: 33. Prove for a > 0: dx x2 + a 1 tan Ja

A:

Q: Evaluate in x cos x dx. .3 I COS" T

A:

Q: II. Let F(x) = | cos(3t – 1) dt. - sin 1. Find F(0). 2. Find F'(x x).

A:

Q: find dy/dx. g(x) = cos x/sin2 x

A:

Q: In(x) Differentiate the function F(x) =| cos(e') dt (for x >0). 1/a Show and justify your work.

A: Given: F(x)=∫1xlnxcos(et)dt      (for x&gt;0) Leibniz rule states that…

Q: Consider the functions h : R→R and g : R -R defined by h(x) = 72 (5 + arctan(sinh 4æ)), . g(x) = 144…

A: Using inverse trigonometric  function properties

Q: Determine f(x) so that cos(In x) f(x) dx = sin(In²x) + C

A: Option B

Q: Find if dy dx y = (cos x) * O (cos x) * (-sin x) O (sin x) * (In cos x - x tan x) O (sin x)* (In cos…

A:

Q: Find F' if rsin ) = /" 4 nin" t t. F(x) = cos-lr

A:

Q: Evaluate (cos x)(n sin x)dx. А In V sin x + C В sin x (1 – In sin x) + C C sin x (1 + In sin x) + C…

A:

Q: Given that f(x, y) - cos(x²) + 6e* sin y . Find fxyxyx · %3D

A: fx, y=x61+6y-cosx2+6exsiny Partially differentiating with respect to x, we get…

Q: There is a unique point a between where the function f(x) = sin x + 2 Cos a and 4 changes its…

A: Given f(x)=sinx+12cos2x Find Concavity  and Find πa

Q: 13. ebx cos x dx exists only when b < 0. lim t→∞

A:

Q: If f (x) = - cos(x), then f (0)(x) is equal to A - sin(x) B - cos(x) В © sin(x) D cos(x)

A: We have to differentiate the given function 9 times

Q: 2T COs x dx

A:

Q: Determine the extreme values of the function f(x) = 2 cos(x) –1 on the interval [0, 27].

A:

Q: 3. If w-f(x.y) and x-r.cose, y-r.sin6 Prove that - A + fy ar

A: Given that w=f(x,y) and x=rcosθ,y=rsinθ Prove that ∂w∂r2+1r2∂w∂θ2=fx2+fy2

Q: Find the extreme value/s of f(x) = 4 sin² x − cos 2x on . (³347) 3π 5π 2' 2

A:

Q: Use the closed interval method to find the absolute maximum and absolute minimum of f(x)= 2 cos x+…

A:

Q: 1. Consider the function f defined on [0, ∞), 1 f(x) = sin- x + 0 x = 0

A:

Q: Let f(x,y) = tan 1(sinh (y) + 2020 cos - 'y) + 4xy Calculate

A:

Q: If y = √1 − x² sin¯¹x, prove that (1− x²) ¹ + xy = 1− x². dx

A: We can prove the given the result by differentiating the given function.

Q: 5. Given F(x) tan(t) dt, evaluate F(0) and F'(0). 1+sin(2x) 1+ et-1

A:

Q: Let  f(x) = cx + ln(cos(x)).  For what value of c is  f '(π/4) = 9?

A: Consider the given function, fx=cx+lncosx first differentiate the function using chain rule as…

Q: Let cos 0 + (sin 0)2 with 0 <0 < 2T. Determine any critical points of y on this interval.

A:

Q: on the right. Prompts Submitted Answers D Ssin(3x)sin(4x)dx S(cos(x) - cos(7x)dx} Jsin(3x)cos(4x)dx…

A:

Q: If g(x) f'(x) and if g(x) (cos x - x sin x)e*cosx, then f g(x) tan(f(x))dx is x cosx In(e*cosx) +€…

A: