DerermiNe The F(X) = arcsec (3X)

Q: sinh-1 x dx

A:

Q: 4 x c) limx→∞ x2+x-2 sin3x e) limx→o sin2x

A:

Q: sinh x – cosh x + ecoth x dx - sinh?

A: see below the calculation below and final answer

Q: Find the first derivative: y = 3 arcsin(cos 2x) %3D O-7 O -8 O -4 O-6 O-5

A:

Q: show how to use integration byparts to find integration (arcsin x)^2 dx

A: Let I=Arcsin x2 This can also be written as: I=sin-1x2 Now if we want to integrate above function we…

Q: When is the arcsin function also a square root function

A:

Q: sin(Tæ) lim x → 12 In(x – 11) -

A: The given limit,          limx→12sinπxlnx-11

Q: Evaluate

A:

Q: 5). § sech x tanh-x dx

A:

Q: VT (2x)[sin (2x²)] cos (x²) your exact-value result. Evaluate dx. Show complete pencil-and-paper…

A:

Q: f(x)= sinh¯ (tan 3x)

A: The chain rule of derivative states: f∘g'=f'(g)×g' The derivative of sinh-1x is 1x2+1. The…

Q: 10. g(x) = e*´ arcsin x

A: g(x)=ex2sin-1x We need to find the derivative of the given function.

Q: csc squared x/2 = 2/1-cosx verify with steps

A: To Verify:

Q: sech (In x*) 15. dx x/6 tanh (In x2) – tanh? (In x2)

A:

Q: te dt lim 0 x-0 sin x =?

A:

Q: sin(2x) limy→ 0+ X

A: Given:     limx→0+sin2x2

Q: sec (x) tan (x) dx S S cos(x) sin (x) dx - log2 (x) dx

A: Important points: 1. If the derivative of a function is present then assume the function as t and…

Q: sinh x + cosh x)ª= e4x

A:

Q: x-sinx 1. lim X-0 x-tanx

A: Given function is limx→0x-sinxx-tanx

Q: (b) lim ln(sin x) x→0+

A: b) limx→0+ln(sin x)

Q: Find the indefinite integral ∫x arcsin x dx

A:

Q: 1 lim (1 + sin²x)x

A: We have to solve the given limit: limx→01+sin2 x1x This is 1∞ indeterminate form of limit we know…

Q: -e lim te Int - 1

A:

Q: l = lim x→0+ In(x)

A: No, its wrong. you are correct limx→∞ln(x)=-∞…

Q: sin 2x ind lim X-0

A: Given that: 1. limx→0sin-12xx2. ∫x(x-2+x3)dx

Q: ldx on the graph y sec x? + y? = cos2x at point (1, 2).

A:

Q: = 5 sec x tanx %3D

A: Please refer to the image below

Q: cosxsin2x lim 1-sinx x- 2

A: limx→π2cos x sin2x1- sinx=limx→π2cos x 2 sinx cosx1 - sinx=limx→π22 cos2x  sinx1 - sinx…

Q: y = Arctan (sinh x)

A: dydx=ddx(arctan(sinh x))

Q: sinh-1x = In (x + vx² + 1) %3D

A:

Q: Graph of ln x

A: Given,         The function is fx=lnx.

Q: lim sin3x / tan2x =? x-->0

A: find the value of

Q: sin5x(1-2t)dt (6) lim

A: limx→0∫xsin5x1-2tdtx Let  I=∫xsin5x1-2tdt=t-t2xsin5x=sin5x-sin25x-x+x2

Q: Find the value of : sin3x lim x→0 2x

A: This question is based on Limits.

Q: Solve without a calculator: lim (sin2(3x) / 9x2) as x approaches 0.

A: We write the expression using a square. Then move the limit inside the square. Because the limit…

Q: 1 lim x-0 (sinx ズ→ X.

A: Evaluate the limit limx→01sin x-1x. Rewrite the expression: limx→01sin x-1x=limx→0x-sin xx sin x…

Q: cosh x 2. Find lim. ex

A: We have to find the limit

Q: log, (cot-x) 3. lim 1- cosh(2") X -00

A: limit.

Q: sinh-1 x dx.

A: We can find the answer as below

Q: cos(x)-1 lim-0 sin(x) limx-0 %3D = 1

A: Substituting x=0 in cosx-1xwill result in indeterminate form 00. Use L'Hospital's rule,…

Q: Solve the integral 1 4. arcsin x dx 0.

A: Consider the given integral ∫01arcsinxdx. Let u=arcsinx,      and     dv=1. That implies, du=11-x2,…

Q: limx→0 sin 2x 2x²+x

A:

Q: sinh x – cosh x + ecothx dx - sinh2x

A: Let's find.

Q: Sin²X+SIN 2X 1)Lim 5X x → 0

A: Here we find limit

Q: 5. Carefully explain why 2 arcsin(x)+2 arccos(x) : Hint: How can we tell a function is constant from…

A:

Q: sec² x 12. S 1+tanx

A: here we use       ddxtanx=sec2x see below the calculation and answer s

Q: etan x dx 1 – sin²x

A:

Q: 2x lim ¤→0 sin x

A: We have to find limit