e) lim 1-cost sin²)

Q: Using an appropriate substitution, i) Evaluate [x (1- x)³ dr.

A: The solution for the above question is as shown below.

Q: Maximum value (If none write DNE): x = -6 (If none write DNE): f(Max)= 6 X o, value of maximum value

A:

Q: 5. lim (2x² – 5x + 1) x-1 A. 8 В. -8 C. -1 D. DNE

A: We can find the answer as below.

Q: 3.) Given y=5* (2, 1)? which of the following shows the equation of the line tangent to y at the…

A: To find the equation of the tangent line to the curve   at the point .

Q: 2 xe-x* dx 0.

A: Given,

Q: 3. Solve the following equations over the interval [0, 2π]. Use exact values where possible, or…

A: a) tan2x=13 tan2x=13tan x=±13x=π6,7π6,5π6,11π6

Q: Find the tangent equation for the function: f(x) = Vx2 + 5 at x-2?

A:

Q: '] Find the derivative of the function. a) y=c sint+\t cos t b) y = secx+e

A: Tje solution of the problem is given in the next steps .

Q: Use the Quadrature Rule Calculate I = S e2x dx using the 3-point Gaussian Quadrature method.

A: Given integral is I=∫03e2xdx

Q: e* tan (e*) dx sec2 (e*) – 7

A:

Q: Lim (csc y+1)/(1-sec y) a) as y -> pi/2 b) as y -> pi/4 c) as y -> 3pi/2

A: (a) As y -> pi/2, Lim (csc y+1)/(1-sec y) = [csc(pi/2) + 1]/[1 - sec(pi/2)] = (1 + 1)/(1 - 1/0) =…

Q: Q.5: Derive reduction formula of f cot"x dx. Also prove that -cot*x cot2x S cotx dx = + InSinx + C.…

A:

Q: 10 · S (sech u + tanh u)² du

A:

Q: Show that d/dx(x arcsin x+√1−x2) =arcsin x.

A: We separate the differentiation with both parts

Q: Find values of a and c such that the tangent to y = ax2 + 12x + c is horizontal at the point (2,5)

A: Tangent is horizontal where derivative is zero

Q: Find a suitable substitution for evaluating ∫tan x sec2 x dx andexplain your choice.

A: we have to integrate the following integral using a suitable substitution. ∫tanx.sec2xdx

Q: 13, mz1=(x² +7) and mz2 (2x² + 19)".

A: we have to find the angle between the floor and the light beam.m∠1=12x2+7°m∠2=2x2+19°sincem∠1=m∠3now…

Q: n lim dr.

A:

Q: ) Find the derivative of the following: a) sin (4x- 7x+ 3)

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Q5) find the slope of tangent to the curve at the given points: y? + x? = y* - 2x at (-2, 1) and…

A:

Q: 4x 3-limx-0 tan5x sin(cos y) 4-lim, y- 2

A:

Q: 5)find y y= Inl-decx +tanx)

A:

Q: lim →+ 0+ sin 0 sin 0-1

A:

Q: Q1)a) Find line that are tangent the curve x + xy = 1 at the point (-1,0)

A: The given equation of the curve is x2+xy=1 and the point is (-1, 0). Evaluate the slope of the…