Consider the functional S[y] = =ffdx [₁ = dx ln(1 + x²y'), y(1) = 0, y(2) = A, where A is a constant and y is a continuously differentiable function for 1 ≤ x ≤ 2. Let h be a continuously differentiable function for 1 ≤ x ≤ 2, and let e be a constant. Let A = S[y+ ch] - S[y]. (a) Show that x²h' 24h2 A = c ² da 4²² - ² ² dx + 22/7² +0(8³). dx 1 1 + x²y' 2 (1+x²y')²

Q: The doctor prescribes 25mg/kg divided into 3 equal doses for a todddler whom was 42 lbs. find the…

A: The weight of the child is 42 lbs The weight of the child in kilograms is 42×0.4536=19.0512≈19…

Q: f is a differentiable function. Then (х) dx ef(x) + C el(x}+C f'(x)ex) + C f'(x) + e(x) + C f(x)ex)…

A: topic - integration

Q: If y = f(x), then f'(x), y', [Select] dy da and f(x) all represent the of fat x.

A: If , then to determine the meaning of .

Q: vativ point

A:

Q: Differentiate fx) with respect to g(x) of yx= xsiny

A: To find the derivative

Q: d g(s) be two differentiable functions in R and f  (2) = 8, g(2) =0, f(4) = 10 , and g(4) = 8 Then…

A:

Q: If some function f(x) has a relative extrema at the point (c, f(c)), then f'(c) = 0 True False

A: if we want to fine any fuction has relative extrema then

Q: Let a 0 for all x = [a, b]. Let A > 0, B > 0 be constants. S[y] = is given by y(x) [* dx ƒ(x) √ 1 +…

A:

Q: Consider the functions f(t) = e' and g(t) -81 defined on 0 st<o. %3D = e (a) (f* g)(t) can be…

A: Consider the functions, f(t) = et and g(t) = e-8t

Q: Show that the functions f (x) = I x I and g(x) = x 1/3 are not differentiable at x = 0

A: Derivative of x at x=0:   Plotting: x,  xx

Q: Let f(x) be a differentiable function. Explain why it is possible that f'(c)=0 for a function but…

A: Let f(x) be a differentiable function.

Q: Let H(x) = f(xg(x)), where f and g are differentiable functions such that g(2) = 3, g' (2) = 5, and…

A: We will solve the following.

Q: Assume that f(x) and g(x) are both differentiable functions. Given f(3) = -2, %3D g(3) = -4, f'(3) =…

A: f(x) and g(x) are both differentiable functionf(3)=-2, g(3)=-4, f'(3)=8 and g'(3)=2h(x)=3f(x)g(x)+2

Q: Determine if f(x) is differentiable at x = 0 if

A: We will find out the required solution.

Q: Let f(x) and g(x) be differentiable functions such that • f(3) = 1, f(0) = f'(3) = 2. • g(1) = 0,…

A: Given, fx and gx be differentiable functions such thatf3=1f0=2f'3=2g1=0g'1=2 Used differentiation…

Q: If f and g are differentiable functions on (-oo, o0), then y = f(g(x)) is differentiable everywhere…

A: This question related to derivative.

Q: Let a differentiable function z = f(h²(x² + y3), 2łn(x +y)) satisfying the condition f(4,0) 1 be…

A: We need to find the partial derivative of z with respect to x for the given function.

Q: Let a 0 for all x = [a, b]. Let A > 0, B > 0 be constants. S[y] = da [* dx f(x)}√/1+ y^², _y(a) =…

A: Given functional is where  is continuously differentiable function on the interval So to get optimum…

Q: Let f and g be functions differentiable on R. with Find f(x)|x=2= d g(2) = 2, 9(x)\x=2 = 4, de…

A:

Q: Find the zeros of Q(x) = 5x - x² + 9 using the quadratic formula. Number of zeros: one

A: Given Quadratic formula is Q(x)=-x2+5x+9 Compare to ax2+bx+c=0 Here a=-1, b=5 and c=9.