Suppose that f(0) = 1, f(0.5) = 2.5,f(1) = 2, and f(0.25) = f(0.75) = a. Using trapezoidal rule with n = 4 gives f(x)dx= 1.75, then a= %3D Select one: а. 2.5 b. 1.5 C. 4.5 d. 3.5

Q: By definition, (f ° g)(x) = f(5) = 12, then (f°g)(2) * So if g(2) = 5 and %3D %3D %3D

A: By definition, f∘gx=fgx

Q: Find the da/dx, where a is a function of x: a²x² + 2ax = a.

A: The given function,        a2x2+2ax=a

Q: Given a function f(x,y,z) = 2x2 In (6y + 3z). Find the range of the function.

A:

Q: If L(f(x) – 2g(x))dx = 12 and g(x) = x, find f(x)dx. Hint: draw a sketch of g(x)! %3D

A: We have ∫28(f(x)-2g(x))dx=12g(x)=xWe have to find∫28f(x) dx

Q: The range of f(x, y) = – Vx2 + y? is %3D Select one: a. R? x b. [0,00) C. (- 00,0] |

A: We have to find the range of fx,y=-x2+y2 .

Q: Q1: Find A: fxx fyy and fxy for the following functions f(x,y)= In(tan-¹xy)

A: Let us consider the given function z=f(x,y) The first order partial derivative are ∂f∂x,∂f∂y The…

Q: If f(x) = x – Vx – 2, find all values of x for which f(x) = 4. %3D

A: fx=x-x-2

Q: What is the length of EF? y 4 8 units 10- 7 units 4 2 units -10 -8 -6 4 10x -2- 6 units -4- -6 -8

A: solution of the given problem is below ...

Q: the extremum of f(x,y) = 7x²y² +5y² 9x?. +

A: Given that: f(x, y)=7x2y2+5y2+9x2

Q: Assuming 0 < c < d, find the value of b (in terms of c and d ) for the function given

A: given: 0<c<d. the given integral is∫cdx+bdx=0 ∫cdx+bdx=0x22+bxcd=0d22+bd-c22+bc=0

Q: Q5: Differentiate the following: a. f (x) = In(3x + 2)5 b.y = (2x* + 1)tanx c. f(x) = etan(2x)

A:

Q: Use the function f(x) = Vx and a starting point of a = 8 with linear approx- imation to approximate…

A:

Q: E (x+1) xp:

A: Given integral is, ∫x+112x52dx.   It is integrated as follows:   Apply u-substitution: u=x+112…

Q: If f(x)dx = 5, f(x)dx = 2, and f(x) dx = -1, find f(x)dx. %3D %3D %3D ... А.) —2 В.) 2 C.) -3 D.) 3…

A:

Q: 15 f(x)dx%3D 2 f(x)dx =5, then f(x)dx=? Hide answer choices A 25/2 B 5/2 C 19/2 9/2

A:

Q: f(x) dx = 18 and f(x) dx = 3.7, find f(r) dr.

A: using property of definite integration

Q: (2g(x)-3, xsI x>1" "rx)dx = 18, then g(x)dx = Let f(x) - %3D A) 5. B) 6. C) 7. D) 8. E) 9. A) B) c)…

A:

Q: Show that: (e) (VF) = 1 dx

A: Derivative of a function xn: ddxxn=nxn-1                               (1) Given function is: f(x)=x…

Q: If f(x, y) = Vx³ + y³, %D t. find f(0, 5).

A: Given: To find:

Q: dz IV. Suppose z is a function of x and y, and ax² – y? = 2"e6y. Solve for dx

A: Given: z is a function of xand y and x2-y2=zxe6y. To find: ∂z∂x

Q: f (x) dx=6, f (x) dx=2, and f (x) dx= -3, find f (x) dx. If 2. 2. A -3 B) 4 3.

A:

Q: If f(x) dx = 4x° – 7x° + C, find f(x). %3D f(x) = %3D

A: We are going  to find f(x)

Q: then A(-2u - 20) = -2 ---B 5 and Au 3 Au = 2 4

A:

Q: Find the domain and range of the functions: 2) f(x) = /4 – Vx

A: f(x)=4-x

Q: Find dy for the following functions: - dx 6 1) у - 2 y = * 1 1 Vz² 8x4 2x8

A: 1) y = xn     dydx = nxn-1 2) y = 1x      dydx =-1x2 3) y = z     (a) if z is constant…

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.