Differentiate the following functions: d a) dz (- 4 sec( – 10z")) = d :(V-10 cot x) dr b) d c) (- 4 tan( – 3r¯1º) · – 50log, x) 3x5 d d) dr 10 csc(3x) ||

Q: Eliminate the arbitrary constant for y = 2 + Cq sin 4t

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Q: Show that the two formulas are equivalent                                                   ∫sec x…

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Q: 4. у%3D 5/(sin3x +сos3x)

A: y = 5sin3x+cos3x

Q: Show that for n > 2, tan x sec"-2 п — n-2 T dx . sec" x dx sec"- п — 1 п — Use this to find sec x…

A: ∫sec4x dxWe need to find the integration by using the given formula.

Q: Q5. If x- a.sec 0 and y -b.tan 0. Eliminate 0.

A: It is given that x=a sec θ  and y=b tan θ . So, xa=sec θ and yb=tan θ.

Q: cosx t cost (a) f(x) = (b) у %3D 1+ sinx 1-t

A: Follow next step

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A: We have to solve the problem

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Q: Express cos°x as a function of multiple angles.

A: The function of multiple angles is given below,

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Q: sin 4y w = y+1

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Q: prove that  d/ dx ( sec x) =sec x tan x

A: We have to prove ddxsecx=secx tanx We know that secx=1cosx So, we have to differentiate ddx1cosx…

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A:

Q: Let f(æ) = - 6 sin(x)cos(x). %3D df dx d²f da?

A: Using product rule, (uv)'= u'v + v'u Here we take, u = sinx v = cosx df/dx =(uv)'…

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A: Given that f(x)=cos-1(5x) Find f'(x)

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Q: Find f'(x) given トhat fcx)= tan Cax - Jx +4ょ3) %3D (assume real number) is

A: Our aim is to find f'(x) where f(x)= tan(ax5-x12+4x-3), where a isassumed to be a real number.

Q: tan x sec? x dx

A: Given integral: ∫tan2 x sec2 x dx

Q: Let f(x) = sin x and g(x) = ex. If y = f(g(x)), what is y'(0)?

A:

Q: Find a function F(x) satisfying F'(x) = sin(6x).

A: Solution  Let consider differential  F'(x)  of function F(x)  so F(x)=∫F'(x)…

Q: Find f'(x) where f(x) sin(cos(4x2 +1))

A: Consider the given function

Q: Consider the function f(x) whose second derivative is f"(x) = 7x + 10 sin(x). If f(0) f(x)? 3 and…

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Q: Calculate f/2 ( sin a) da xp

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Q: Derive a formula for tan x sec" x dxr where n# 0.

A: Please go through the attached solution. I hope that this solution will help you. Thankyou . Best…

Q: use a geoetry formula to find the exact value of the definite interval (-2x+4) dx on the interval…

A: The given function is (–2x+4) with the interval [0,3].

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A: We have to fill in the blanks: As θ increases from 0° to 90°, the value of cosec θ tends towards…

Q: Consider the function f(x) whose second derivative is f"(x) = 10x + 10 sin(x). If f(0) = 4 and f'(0)…

A: Given that: f''(x)=10x+10sinx

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A:

Q: If f(x) = 2x(sina + cos a), find f'(x) = %3D

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Q: (B) Evaluate tan (3.x +1) sec³(3x +1) dx

A: In this, We find the value of the given integral using tan^x+1=(sec^2)x formula.

Q: 3. f10x-sec(5x) tan(5x²)dx ans : sec(5x²) +c (VF). cot 4. dx ,note: Vx = xr ans : 2 In

A: ∫10x·sec(5x2)tan(5x2)dxlet u=sec(5x2)du=sec(5x2)tan(5x2)·10x  dxdx=dusec(5x2)tan(5x2)·10x Replace dx…

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A: We know thatddxtan-1x=11+x2

Q: y = 5x – 6 tan x, concave upward concave downward

A: Given problem:- y=5x-6tan(x) , (-π/2, π/2)  Determine the open intervals on which the graph is…

Q: tan³ (In x) sec (In x) dx (8)

A:

Q: (b) 는(cosx)=-sinx (d) VI+ tan x 1+* Q1) Show that: (a) (1+x) =1+6x (e) (V): *- () %3D

A:

Q: dx is equal to 1+cos x O - cotx + cscx +c O - tanx + cscx + c O - cotx + secx + c O cotx + cscx + c

A: We have to find the integration and also find the limit in the second question.

Q: If f(y) tan (2y'), find f'(y). Use exact values. f'(y) =

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Q: If f(y) = tan- (3y*), find f' (y). Use exact values. %3D f'(y) =

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Q: Find f(x), where f'(x) = sin(x) + cos(x) +1 and f(7) = 2.

A: Given: f'(x)=sin(x)+cos(x)+1 and f(π)=2

Q: ind the second derivative and simplify the final result 1. cos(xy) + sec(y) = 5

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Q: d (sec x) dx 18. Prove that = sec x tan x. %D

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Q: mpute the following derivative. [(3fi+ Vij- 4 'k) (cos ti+ sin 2t j- 31 dt (3?i+ Vij- 4t-'k) • (cos…

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Q: Use 2- step substitution St* sin (t5) cos(t5)dt

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Q: Find the tangent of 2X. Х. 13 Y 12 Write your answer as an integer or as a decimal tan (X) %3D 5.

A: this is the right triangle

Q: Let f(x) = - 8 sin(x)cos(r). df dr d²f dz?

A: Let fx=-8sinxcosx. Then we have to find dfdx, d2fdx2.

Q: 1. Differentiate each function by using formulas. t cost (b) у %3D COSX (a) f(x) = 1+sinx

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Q: What is y = sin (xy)

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Q: Differentiate each of the f cosh(x)+1 cos(r)+1 a. Y =

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Q: Differentiate the following x 2 tan(y) + y 10 sec(x) = 2x

A: Given that

Q: Write Vx+36 as a function of 0, where 0<0<-, by making the substitution x=6 tan 0. %3D x+363D sin O…

A: Using trigonometric identities :    1 + tan2  x = sec2 x

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.