When applying substitution (u=tan(x)) to [s sec¹(x) tan(x) dx is equivalent O a) [ (u³ + u) du O b) [ f (u³ – u) du 1 (205 (u³ + u) du O c) Od) / (u²-u) du

Q: Find all solutions to tan(x)=sec(x) that lie in the domain [0, 2)

A: tan(x)=sec(x) Given interval is [0, 2).

Q: Let f(x) = (sin(x))*. Find the value of (a) 1 (b) 2 (c) 2 (d) 2 (e) 0

A: The given function is fx=sinxx. To find the value of f'π2, first take the logarithmic of fx=sinxx on…

Q: Differentiate g(x) = (In(x² + 1) – tan-ª(6x))10

A:

Q: Sketch the region of the enclosed by thes curves x = e and Y = . Set up the integrals both in terms…

A: Region enclosed by curves x=ey and y=x-1e-1

Q: 3. Find the derivatives: 3x3-4 a) f (x) = b) y = (x2 + 6x + 2) (+ Vx5 + 3) DO NOT SIMPLIFY 2x²+3 c)…

A: a) Use quotient rule of derivative and find the derivatives of above function.

Q: Evaluate sec³ (0) tan³ (0)dē. ○ sec (0) - sec³ (0) + C ○ sec³ (0) + sec³ (0) + C O sec³ (0) + sec(0)…

A: Step 1:To solve the integral ∫sec5(θ)tan3(θ)dθ, we can use substitution and trigonometric…

Q: Compute Each Derivative: 1) d tan¯¹ (1 + e²x) dx 2) x²cos-¹(3x4) d dx 3) x(sin-¹(x))² dx

A:

Q: 3. Find the derivatives: a) f(x) = 3x³-4 2x²+3 b) DO NOT SIMPLIFY y = (x² + 6x + 2)(²+√x + 3) c)…

A: Given; a) f(x)=(3x3-4)/(2x2+3) b) y= (x2+6x+2)(2/x4 + 3sqrt(x5) +3) c) g(x)=-2csc7x+8sin3x+12tan2x…

Q: b) Find the points at which the function f: C → C defined as: f(x + yi) = x - yi Have a complex…

A: To find the points at which the function f(x + yi) = x - yi has a complex derivative, we need to…

Q: Q# (13 Rewrite: cos (x)sin(x)dx A) ſ u'du 1/2 B) Tu°du V312 C) [ -u°du 1 V3/2 D) [ u°du 1 V3/2 E)…

A:

Q: Question 2 * SE sec2 (0) d0 = dx a) sec² (x³) - 3x² b) – sec² (x³) · 3x? | O ) sec² (x³ ) d) – sec²…

A:

Q: 2. The suitable Trignometric substitution that solves fx(x-2) dx is (x-1)=sin 0 x-1)3sec0 (x-1)=tan…

A: We can find the answer as below.

Q: Find linearizing ( L(x) ) f(x) at x=a . where f(x) = tanx and a = π a) π b)  x - π c) π - x d)…

A: SOLUTION-

Q: Using the substitution t tan can be written as of dx sin(x) - 60 cos(x) of dt +30-30 2 de 30²2²…

A: I am attaching image so that you understand each and every step.

Q: Evaluate tan" (x) sec4x dx. 1 1 (A) =tan(+3)(x) + _____tan ( + 1)(x) + C m+3 m+1 1 B) (m+3 -tan…

A:

Q: a) f(4x)dx x)cx

A: ∫02f4xdx Now, solve the above integral, ∫02f4xdx=∫01f4xdx+∫12f4xdx=f4·1-f4·0+f4·2-f4·1=f8-f0=1-0=1…

Q: 1. Find the natural domain and the derivative of the given function. (a) 3x² +7x + 5, (b) (3x +1)5,…

A:

Q: If, for V = V (t), tsin(V) = cos(V)+ In(t), then: a) V'(t) = 1 – tsin(V) t(t cos(V) + sin(V)) b)…

A:

Q: : (a) Evaluate S cosx sinx V1 – sin+x_dx. (b) Evaluate S V1 – x² dx.

A:

Q: 5. Evaluate | (x² +1)* dx using trigonometric substitution as your first step (not a u-sub as your…

A: The solution is given below in the next step:

Q: (a) [In(4) - 2e¹³] dx d b) dx d (c) [2²² - 1 (2²)] = 4e³x In(x [sec (12r) + tan-¹(2x)]

A: NOTE: Refresh your page if you can't see any equations. .

Q: Show that d 1 In cos(x) os(x) - csc(x) dx 1+ cos(x

A: We have to proof