If f is a positive function and f"(x) < 0 for a < xs b, show that T, < f(x) dx < M,

Q: Q2: - If y = 3 sec3t and x = etan3t prove that: - dy (In3)² ,Y logy x %3D dx

A:

Q: If f(x.y) = In(x² + y²) + find fr and fy -

A:

Q: The linear approximation at x 0 to sin(2x) is A + Bx

A:

Q: 2. dy sin x - y where f(n) = 0. %3D dx

A:

Q: if f(x)=2x-cos(x), Use Newton's method to approximate x, starting from the initial value xo=0

A: Solution:-    fX=2x-cosX           x0=0    f'x=2+sinxwe know      x1=x0-fx0f'x0           =0-f0f'0…

Q: sin(t) dt , 1-4x 1+ t2 4 If f(x) then f' (x) =

A:

Q: find the antiderivative F(x) of f(x)=x^2+sin(x)+3 with F(0=8

A:

Q: If y=sin-1x then dy/dx= 1/dx/dy for all x in [-1,1] True or False.

A: Given statement If y=sin-1x then dy/dx= 1/dx/dy for all x in [-1,1] is false.

Q: Evaluate f(x) dx, where f(x) = 13 sin(x), 0< x < T. f(x) dx =

A: The solution is given as

Q: Let f(x, y) = sin(3x + 5y) and P = 3 Find the maximum rate of change of the fucntion f at the point…

A: Find gradient of f(x,y). Find compute the point . Take the magnitude of the same .

Q: Find f(x), the most general antiderivative of the function: f" (x) = 18x – 3 sin(x)

A: Explanation of the answer is as follows

Q: dy Prove that dx of x2 +2x is f'(x)=2x + 2

A:

Q: (a) Show that the derivative solution of this function y = x** is dy = x(**+x=1) [1+ x ln x (In x +…

A: The given function y=xxx Note:    Multiple questions are given, we are answered with only one…

Q: find the absolute extrema of thefunction on the closed interval y=x \ln (x+3),[0,3]

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents…

Q: Find the solution and the interval of existence for: (1-x2)dy/dx + 2y = (1-x)2

A:

Q: Find the length of the curve y =x2/8 − ln(x) on the interval [1, 2].

A:

Q: 3 f(x) dx = 4, find | xf(x*) dx. If f is continuous and

A:

Q: find ∇f at the given point. ƒ(x, y, z) = (x2 + y2 + z2)^(-1/2) + ln (xyz), (-1, 2, -2)

A: Given function is  Firstly, we find all first order partial derivatives of f

Q: Some elementary functions, such as f(x) = sin(x2 ), do not have antiderivatives that are elementary…

A: let ∫x-necxdx for n a positive integer and c a non zero constant is non elementary since…

Q: The linear approximation at x 0 to f(x) = sin(6x) is:

A:

Q: Find the solution and the interval of existence for  (1-x2)dy/dx +2y = (1-x)2

A: The objective is to find the solution and existence for  1-x2dydx+2y=1-x2dydx+21-x2y=1-x1+x The…

Q: If f(x,y) = y2 ex + 3 ln (xy), find fxyy (1,1). fxyy (1,1) = ?

A:

Q: 1. If F(x)= = cos a sin r (√t-1)' dt, find F'(x).

A:

Q: 5. Given F(x) = cos (t) dt, determine F'(x). 2

A: Using leibniz rule  Explanation is given below....

Q: If f =x-e" and F=x'yi-2y'zj + xy'z'k, find: div(F x grad(yf )) at (4,1,-2)

A: The function                     Then, we have to find

Q: Evaluate the function: S de x(x-2) -dx (x–1)³

A:

Q: 1. If F(x)= = ² e²² et² dt, find F(1) and F'(x). ez

A:

Q: If f(x) = x^2 sin(3x), find the differential dy

A: Consider the given: fx=x2sin3xy=x2sin3x Differentiate w.r.t. "x", dydx=ddxx2sin3xApply the Product…

Q: If f(x) = – x Find: S",(f(x))² dx That is find S"(: ,(1 - x)?

A:

Q: If sin(x) f(x)= V2+t2 dt tan(x) and g(y)= f(x) dx g" (4) Then is equal to V5 - 2 V3 - 2V3 11 E- 2V3…

A: Given:            f(x)=∫tanxsinx2+t2dt  and g(y)=∫1yf(x)dx

Q: d 1+ tanhx - Show that dx V - tanh x

A: To show: ddx1+tanhx1-tanhx4=12ex2 Simplfiying 1+tanhx1-tanhx,…

Q: Let h(x) = e*. f(x) and assume that f(ln 4) = -5 and f'(ln 4) = 6. Find the equation of the line…

A: We have to find equation of the line tangent to y=hx when x=ln(4)

Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) L(x) =

A:

Q: If y = V1-x² sinx, prove that (1–x²) +xy =1– x². dx

A: Given that :- y=1-x2sin-1x Prove that :- 1-x2dydx+xy=1-x2

Q: The of the function y= e sin(3x)- In(5.x +2x+1) dx at (0,0) is: А. О В. -1 С. 1 D. 3

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: If f(x) = S dt for x 2 1, find f'(2). 1+lnt

A: Simply use the formula for the derivative of an antiderivative.

Q: The function f(x)=|x|·sin(x) is differentiable at x=0.

A:

Q: The function f has a continuous derivative. If f (0) = 1, f (2) = 5, and f (x) dz 7, what is %3D %3D…

A:

Q: 11) Find a function y-f (x) that satisfies both conditions: d - 6x -4x+5,f(-1) =3 dx %3D dy 2 3 ==+…

A:

Q: Limit 0 to 2 √x dx

A: We have to find the definite integration: ∫02xdx We know the formula of integration, ∫xndx=xn+1n+1+C…

Q: Suppose f(x) = x² + sin æ and F is an antiderivative of f that satisfies F(T) = 0. Then F(x) =

A: Solution..

Q: 2. In each case, find the derivative d. (a) z = x³ – y² and x(t) = cos 2t and y(t) = e-3t, (b) z =…

A:

Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) = sin(x), a = 2…

A:

Q: Show that d/dx(ln kx) = d/dx(ln x), where x &gt; 0 and k is a positivereal number

A:

Q: Find the general antiderivative of the function f(x) = +3 sin x - : 1 1+x?

A:

Q: [a, b]. If F(x) is an antiderivative of f(x), for real numbers ¤) + k]dx is equal to

A:

Q: Find the first derivative 1. y = In v4-x2 %3D 2. In(x2 + y2) + 4arctan = 5 y %3D dy x+4 3. Find , if…

A:

Q: 9. If f(x,y) = -cos x+e*y, find Vf(x, y).

A: For the solution follow the next step.