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

Q: If F(x)=sin(7-x5-13-x³ +5-x). Calculate dF(x) = dx

A:

Q: Find the derivatives of the functions in Exercis

A: Differentiation of the rational function can be done with the help of the differentiation formula…

Q: What is the 2nd derivative of x9 cos x

A: To find out the second derivative of the function.

Q: If f(x) =sin x sin2x sin3x find f" (x)

A: Given f(x) and find second derivative of this function. We use trigonometry relations and derivative…

Q: S sec*x csc*x dx

A:

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

A:

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: 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: 3x2-7x+8 f(x) = Find f'(x) %3D sin (5x2+9x-6)

A: Here we use division rule of differenciation.

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

A:

Q: Suppose f(x)=x^4+3x+1 on the interval [−4,−1]. Find x when f′(x)=0.

A: Given function is Differentiating with respect to x , we get

Q: Simplify (1/sin (x))+(1/sin^2(x)) in a single reduced fraction

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: 4x - 7x Differentiate with respect to 'x' 6x + 5

A:

Q: Let f(x) 39 27 O 1 4√3 O-√6 9 3√3 .-1 (²). Then the second derivative at x = -1,f"(-1), equals = COS

A:

Q: Find ao of the function f(x) =÷(n - x)2 | О п^2/12 5 T^2/6 5 T^2/12 O T^2/6

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

A:

Q: Find the differential of y = e ³²cos3z (A) dy=3e-32 cos3z B) dy=-3e-32 (sin3z + cos3z) dy = -e-³²…

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: Letf(x) =(6x if 0≤ x ≤2,(−4 if 2 < x ≤6.Find ∫^6v0 f(x) dx.

A: Given information:Here, it is given that f(x) will be equal to 6x if x lies between 0 to 2 and f(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.