for 0sxs 10 for r> 10 sin(x) for 0srs2x for x> 2x

Q: Ssec*x tan*xdx C'

A: We can find the integration as below

Q: 2 cosh x +losion2x = 5

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

Q: If f(x) = = sin (3 – x), then f'(0) O 6 sin 3 cos 3 O 6 cos 3 O -2 sin 3 cos 3 O -2 cos 3 -2 cos O 2…

A: f(x)=sin2(3-x)

Q: If 1 dx = 1 dx 1+ x² 1+ x2 1 dx 1+ x² then || 8. 8.

A: Given, ∫-∞011+x2dx=∫0∞11+x2dx=π2

Q: f(x)=(6+x^3)^cos x Explain with steps

A:

Q: Given f(x) = -5√x fractions. f'(x) = 5 2√√√√x + 3 X من * 8, find f'(x) and its domain in interval…

A:

Q: / If f(x) = 2x (Sinx+cosx) find. f'(x) = ' (5) =

A: Given function  f( x ) = 2x( sinx + cosx )

Q: Check whether the function f(x) = cotx and f(x) = sin2x is well-conditioned or ill- conditioned at x…

A: A function is said to be well-conditioned at a point if small changes in the input result in small…

Q: Problem 1: Consider the following dynamic system: dt x2 e2-5 If the steady state value of the input…

A: Ans 1.

Q: d Verify tanh - = X 1- x2 dx

A: Inverse hyperbolic tangent function can be expressed in logarithm funtion. Write tanh-1x=12ln1+x1-x…

Q: Find f    if  f'(x) = 7x9 − 5 √x + 3 sin x,   f(0) = 4

A:

Q: Show that cosh (3x) = 4cosh³r - 3 cosh T.

A:

Q: If f (x) = -4 sin x – 6 In x, find f'(x). f'(x) =

A: The given function is f(x)=-4sinx-6ln x

Q: B₂ (x₂3x₂ ) = 4x₁x₂ *1*2 0< x₂ <1 2 Y₁ = x₂₁² Y₂ = X₁ X/₂ Find the joint pdf for Y₁, Y₂ for 0<x< ₁…

A:

Q: Show that the function f(x)=x^-4 +cos(-2x) is even, odd, or neither."

A: Given, f(x)= x^-4 +cos(-2x) f(x)= (1/x)4 + cos(-2x)

Q: Given f'"(1) = – 4 sin(2x) and f'(0) = 2 and f(0) = 1. Find fG): sin(7 + 1)

A:

Q: Find f'(x) for each of the following sin-¹ (5x-2) a) f(x) = 10

A: Given  fx = sin-15x-210 We have to find f'(x).

Q: If f(4) 8 and f '(x) 2 1 for 4 < x < 9, how small can f(9) possibly be?

A: Given:- If f(4) = 8 and f '(x) &gt; 1 for 4 ≤ x ≤ 9 To find:- How small can f(9) possibly be?

Q: Plot the following function 0 <x< T sin(x) f(x) = } -0.81x2 + 7.64x – 16 π<x< 2π -1.62x2 + 25.46x –…

A:

Q: 1- 1- (Sin (coshx) sinhx dx

A:

Q: y(x) = aox -1/2 X - x3 3! x5 5! = ao sin x x1/2 (4

A:

Q: If a = 1 − v^2 and both x and v are zero when t = 0, show that x = −1/2ln(1-v^2) and hence find v^2…

A:

Q: Use False Position method to Find the root of f(x) = sin(x) - cos (x) . Use a tolerance of 10^-7 if…

A: Given   : f(x) = sin(x) - cos(x)To find:  'xn' such that f(xn) &lt; 10-7 Method:1. Finding first…

Q: O find fx) if CoSx @ £(x)=. Sin X O flx) = x-4CSC x+2 Cot X © f(x)= (x).cotx 3- COSX. CSCX

A: SOLUTION-

Q: Let f(x) = -2x√√x + f'(x) = -8 x²√x

A:

Q: (2.00-x) Vq₂ = ±xV|q₁|

A:

Q: solve for x if CDy=4(x-E)

A:

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.