2. Let a > 0 be a fixed real number. Determine whether dx xl+a [3 converges or diverges. If it converges, then find its value.

Q: 10. f x¹ In x dx

A: To find the integration of ln(x).x^n

Q: Suppose that f(x, y) = x² − xy + y²³ − 4x + 4y with D = {(x, y) |0 ≤ y ≤x≤ 4}. 1. The critical point…

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Q: If f(x₁) 0 and f(x₁) > 0 then f has a A at x₁. If f¹(x₂) = 0 and f11(x) < 0, then f has a A at x₂. =

A: As per second derivative test:   If f'(a)=0 and f''(a)&gt;0 then f has a local minimum at x=a.   If…

Q: For the following graph, identify the points where the local and absolute maxima and minima occur.…

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Q: = = 2.3219andlog, y = 2.8074. Given log, a Evaluate log, a

A:

Q: 5. Evaluate the following limits. 1 a. lim X-4+X-4 3-x² x→∞ 2x²+1 b. lim

A:

Q: so whats the answer

A: So what's the answer.

Q: Consider the function f(x) 1 - 7x a. Find the Maclaurin series for f(x). f(x): = ∞ = n=0 JI Interval…

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Q: e the linear inequality. Express the solution using interval notation. 2(8x1) 14x + 10

A: We will find the required.

Q: Find the differential of the function f(x, y) = −2x² + 5xy + 4y² at the point (5, 1) using Ax = 0.25…

A:

Q: The following is a graph of a logistic function P=(L)/(1+Ce−kt) The marked point (25.60,17.5) is…

A: The solution is shown below-

Q: Consider the linear system y' = Aỹ with (a) Find the general solution. 1 4 = (-5₁3) A -1

A: To find the general solution of the linear system y' = A y, we first need to find the eigenvalues…

Q: Find the critical point(s) of the function. f(x) = x-²-5x-¹ (Give your answer in the form of a…

A: Given :- fx=x-2-5x-1

Q: Consider the function f(x)= x - 4ln(x) with an interval [0.25<x<8]. * The global maximum value is?…

A: Here we have to find the global extrema.

Q: Find the particular antiderivative that satisfies the following conditions: F(x) = F'(x) = x³ +8√√x;…

A: F'(x)=x3+8xF(1)=-1∫xndx=xn+1n+1+c

Q: Find the values of x for which the series converges. (Enter your answer using interval notation.) 00…

A:

Q: Let f(x) = 6x² - 4x + 2. Find a constant c between 1 and 9 such that the value of the function f(x)…

A:

Q: Write an equation of the form y= A· b + k for the graph sketched below: -5 -4 -3 -2 -1 f(x) = 8 7 6…

A:

Q: Find a value of c> 1 so that the average value of Ax) = (²) cos(4) on the interval [1, c] is -0.9.…

A: Given function:- fx=9πx2cosπx

Q: Assuming that we are drawing five cards from a standard deck of 52 cord duck . How many ways can we…

A:

Q: (a) by interpreting it in terms of areas. Show the graph! (b) [VI6=240 f(x- (x + √81-x²) dx

A:

Q: Problem 3. Find all points (x, y) on the graph of x² + y²/3 = 8 (see diagram) where lines tangent to…

A: To find the points where the tangent line has a slope of -1, we need to take the derivative of the…

Q: Find the tangent plane to the equation z = = 4y cos(6x - 5y) at the point (5,6,24)

A:

Q: The average value of the function f(x) = (2) cos(4) on the interval [2, 20] is: sin(x/20) A) B) C)…

A:

Q: Find the absolute maximum and absolute minimum of the function f(x)= (2x 5/2)/5) − (2x(3/2) /3)−3…

A: For  a function y=f(x) defined in the interval a,b we find the value of the function at x=a, x=b and…

Q: Consider the function f(x, y) = 2ye" and the region R = {(x, y)|0 ≤ x ≤ 1,0 ≤ y ≤ x³}.

A: Given: f(x,y)=2yex7

Q: Differentiate the following function: f' (t) = f(t) = √t – .

A: f(t)=t6-1t6d dt(tn)=ntn-1we know ba=(b)1a

Q: The sum of two nonnegative numbers is 500. What is the maximum value of the product of these two…

A: The sum of two number is 500. The product of two number is absolute maximum.

Q: 1 Find the area of the surface generated by revolving the curve x = 3 cos (3t), y = 2 + 1 sin (3t)…

A:

Q: (d) S1²= 0 xVx²+4dx

A: According to bartleby guidelines we supposed to do the first one of multiple questions  kindly…

Q: A jet is flying through a wind that is blowing with direction N 30° W. speed of 50 mi/h in the…

A: Velocity vectors÷ For wind  w→=50(sin30 i +cos30 j ) For jet  v→ =775(-sin30 i + cos30 j )

Q: Find the particular antiderivative that satisfies the following conditions: dR dt R(t) = 80 t² ;…

A: Given, dRdt=80t2  R1 = 20  We have to find R.

Q: A projectile is launched from ground level. After t seconds its height in metres above the ground is…

A:

Q: Below is the graph of y = f(a). Find 5 5 f(a)da. Round your answer to three decimal places. 10 d.

A: Solution:  ∫010f(x)dx represents the area under the curve x: 0 to 3 Area= 3×2 =6 x: 3 to 4 Area =…

Q: 37. lim x40+ log₂ x log, 3x

A: Note: Since, the student has mentioned to solve question no. 37,  so we solving according to this…

Q: The general solution to the differential equation. expression for f (x) and its domain? A (В C D…

A:

Q: Find the derivative of the function. f(x) = (tan³(x) + 2)² f'(x) = [] X

A: to find the derivative

Q: Find an equation of the line tangent to the curve defined by a³ + 5xy + y = 7 at the point (1, 1). Y

A:

Q: The desert temperature, H, oscillates daily between 36°F at 6am and 76°F at 6pm. (a) Write a…

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Q: (a) Use logarithmic differentiation to find the derivatives of the followin x. cos²x e (1) Y x² + x…

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Q: Verify that the function is a solution of the initial value problem. (a) y = x²(1 + Inx): y" =…

A: Given:y=x23+x-1   We are required to find: If y is the solution of the initial value problem…

Q: Find the values of x for which the series converges. (Enter your answer using interval notation.) 8…

A:

Q: 11 1+6 2-5 19. 21 -<6 3 s1

A: (19).The given inequality is:x+6x-5≤1

Q: Example: If R is percent of maximum response and x is dose in mg, the dose- response curve for a…

A: Given that curve for a drug is given by R=1001+100e-0.1x

Q: Find the slope of the graph of the function f(x)=√√2x at (18,6). Then find an equation of the line…

A: To Find : Slope of function f(x)=2x   at  (18,6)

Q: Recall that if the cost of producing x units is CO), then the average cost function is Co producing…

A: Given thatFixed costs $100 Variable cost = marginal cost =m=$8

Q: Find the absolute maxima for the function: f(x) = 6 x+ sin (6 x) on the interval [0, 2 π].

A: We have  fx=6x+sin6xx∈0,2π

Q: 1 - cos(x7) x² a. Find the Maclaurin series for f(x) after removing the removable discontinuity at x…

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Q: Find y" by implicit differentiation. 2x³ + 5y³ = 2 y" = 2x² 5y2 X

A:

Q: 9. f sin(In x) dx

A: The given integral is Sin(ln x).