Show that tan(arccosx) for |x| s 1, x + 0.

Q: 14) *Find the arclength of f (x)=x2 on [0,2]. %3D

A:

Q: Find the length of the arc y = In(cos x) between the points (0, 0) and (pi/3, -In2).

A:

Q: Find the arc length of the function y = x2 + x - 2  on the interval [-2,1].

A:

Q: 4. How many fixed points does the function T(x) = tan(x) have? %3D

A: for fixed point f(x) = x x = tan(x)

Q: Find the arc length of y³ + y = x² + 6x on the interval [-5, –1].

A: Since the given graph is in implicit form (we can not find the explicit value of y in terms of…

Q: Find the arc length of f(x) = (1+2²) from x = 0 to x = 2. Simplify your

A: Given :fx=231+x232x from 0 to 2

Q: 2 ind the arc length for f(x) = 6-2 x² over the interval [0, 2].

A:

Q: Determine whether the statement (d/dx) [arctan(tan x)] = 1 for all x in the domain. is true or…

A:

Q: Prove that  d/dx[cosx]=-sinx

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

Q: Find the arclength of y = 2x3/2 on the interval x is greater than or equal to 1 and less than or…

A: Equation of given curve is y=2x32 Differentiate with respect to x. dydx=232x32-1=3x

Q: what is the absolute extrema point(s) of f(x) = e1-cosx on [ -pi/2 , pi ], if there are any?

A:

Q: S cose de 1-sine sece tane de sece - 1 The integral fo fse Si x dx x²+√√√x²−1−1 sino de 1+ cose…

A: we have to above integration

Q: Find the arclength of f(x)=x on [0,1].

A:

Q: Find the total areas of the shaded regions

A: Required area is ∫-π03sinx1+cosx dx

Q: a) Show that the length of the arc of the curve y=f(x) where S(x) = Insecx 0SxS is 4 In(1+ v2)

A: We need to show that the length of the arc of the curve y=f(x) where f(x)=ln(sec(x)), 0≤x≤π4. The…

Q: Prove that 2 arcsin (x) = arccos (1-2x2) for XE (0, )

A: arccos1-2x2 Put x=sinθ, we get arccos1-2x2=arccos1-2sin2θ=arccoscos2θ      ∵cos2x=1-2sin2x=2θ=2…

Q: Find the arc length of f(x) = () (x² + 2)z on the interval [0,9] %3D

A: (6) Given function is fx=13x2+232 and interval is 0,9. We have to find the arc length of fx=13x2+232…

Q: 2 = using the relation r= VT show that sin x %3D EX II

A:

Q: Find the arc length of y = -6x + 2 on [2,5] (use calculus). %3D L = 1 + f'(x)² dx

A:

Q: 4. Find the exact arc length over the interval. a. x= from x = 2 to x = 3 16x2

A: Solution: 4 (a)   y= x6+816x2  from x=2 to x=3

Q: x = -sin 2y x = cos y --

A:

Q: Let f(x) = x^3/3 + 1/(4x) on the interval [1, 2]. Find the arc length. Show all work

A: We find the f'(x) using the power rule

Q: 4. How many fixed points does the function T(x) tan(x) have? %3D

A: As per our guidelines, we suppose to answer only one question. Here question 4) is answared.

Q: Find the arc length of y³ + y = x² + 6x on the interval [-5,–1].

A: The arc length, L of a function, x=f(y) in the interval [a,b] is calculated using the formula below.…

Q: 8. Find the arc length of y3 + y = x² + 6x on the interval [-5, –1].

A: Given equation of the curve is y3+y=x2+6x                     (i) To find the arc length in the…

Q: The f xcos x² 1-sin x2 dx is

A: Given :

Q: Find the arc length of y³+y=x²+6x on the interval [-5,-1].

A: Solution:   Given that,      y3+y=x2+6x,  interval -5, -1         Then, differentiating with…

Q: Find the indefinite integral. ∫arctan x dx

A:

Q: - Find the arc length of f(x) = (-) (x² + 2)ž on the interval [0,9)

A:

Q: Let f(x) = 1/3x^3/2 - x^1/2 on the interval [1,4]. Find the arc length. Show all work

A:

Q: Q: Prove that the arc lenfth af Curve y = log secx from to n- 3 is Use formula Note I+ ( dn.

A: Given: y = log sec x To prove: The arc length of the function y from x = 0 to is .

Q: Find the arclength of y = 3x2 -5 on x is greater than or equal to 0 and less than or equal to 2

A:

Q: find the arc lenght of f(x)= ln(cos x) on [pi/4, pi/3]

A:

Q: Calculate the length of the curve r=a*sin(^3)(x/3) for (x(1)=0, x(2)=3pi)

A:

Q: 1 Use the definition of the hyperbolic functions to prove the identity 1– - = tanh?(2x) cosh?(2x)

A: Explanation of the answer is as follows

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: Given that | sec (x) dx = tan(x) + A and tan(x) dx = ln | sec(x)| + A. Show that O sec2(0) d0 = 0…

A:

Q: Prove that L" (coshat sinat + sinhat cosat) %3D s*+4a*. 2a

A: The function F(s) is Factorize the denominator

Q: |1- x 2 arctan + arcsin(2x – 1) = Hint using f Odx = C

A:

Q: Differentiate: arctan(cosh(x)) Show all working out.

A: to find the derivative of arctan(cosh(x)) proceed as follows we know that ddxtanx=11+x2  apply chain…

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 arc length of f(x) = In(sin(x)) for - 10 8

A:

Q: Find the arclength on y = 4x3/2 from x is greater than or equal to 1 and less than or equal to 3

A: given: the function is y=4x32. we have to find the arc length on y=4x32 from x is greater than or…

Q: The length of the curve y = In(cos x), 0< x <:

A: To determine the length of the curve, y=lncos x, 0≤x≤π4.

Q: The trigonometric integral [sec² x (tan³x - 2 tan² x) dx is equal to

A: SOLUTION-

Q: Find the area bounded by the trigonometric curves y=sinx and 2.828 square units 1.414 square units…

A: Given that curve y=sinx and y=cosx    from x=π4 to x=5π4To find :Area bounded by the region from…

Q: find the intergral of f(x) = sin(x) + cos(2x) on the interval [0,pi]

A:

Q: Find the arc length of the graph of the function f(x) = In(cos(x)) over the interval : 6' 3

A: Given, fx=logcosx,       π6≤x≤π3 The arc length formula of a curve fx between x=a, and x=b is given…

Q: Use Gaussian Quadrature (n = 3) to approximate f(x)dx, where: f(x) = (2.54 - sin0.32x)2 cos0.32x ,…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.