2. Find the derivative: a. y=ln(e^x)/(1+e^x)

Q: Consider the function f(x) = { 4x² =−x+5c_if x ≤ 2 - 4x if x > 2 For what value of c is the function…

A: given function

Q: Solve the exact initial value problem 3y² dx + + (³1²575 2²2 + √²4) · + √2y) dy = 0, y(0) = 2, y5 X…

A:

Q: 5 Determine the difference quotient for the function f(x) = 2x-1.

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Q: An employee's monthly productivity M, in number of units produced, is found to be a function of the…

A: An employee's monthly productivity M, in number of units produced, is found to be  a function of…

Q: Find aw/as and aw/at using the appropriate Chain Rule. Values Function w = y³ - 2x²y s=-3, t = 6 x =…

A: To find  by using the appropriate Chain Rule.Function: Values: To evaluate each partial derivate at…

Q: Consider the function f(x) = 2x³ – 2x on the interval [-5, 5]. (a) The slope of the secant line…

A:

Q: 1) State the order of the given ordinary differential equation. Determine whether the equation is…

A: To state the order of the given ordinary differential equation. To determine whether the equation is…

Q: Consider the following parametric curve. x = sin(t), y = cos²(t); (√2-1) Find an equation of the…

A: The slope of the tangent line to the parametric curve. If x = f(t), y = g(t)   a<= t <= b at…

Q: To test this series for convergence ∞ n=1 n n6 + 7 You could use the Limit Comparison Test,…

A:

Q: For which values of x are the vectors (2x, 4, x) and (-1, -2, x) orthogonal? Select one: O-4 and 2…

A:

Q: In 1993, the moose population in a park was measured to be 3920. By 1997, the population was…

A:

Q: Determine the inverse Laplace transform: F(s) = 4/s2 - 5/(s + 1)

A: To determine the inverse Laplace transform.

Q: Does the set of all positive rationals form a group with the multiplication operation? Either verify…

A:

Q: Let an = 1 for n = 1, 2, 3, ... . Write out the the first three terms of the following sequences. 3n…

A: Given  To find (a)  then find (b)  then find (c)  then find (d)  then find

Q: Use spherical coordinates. Evaluate xex + y2 t2 + dV, where E is the portion of the unit ball x² +…

A: To find  E is the portion of the unit ball  that lies in the first octant

Q: Find the critical numbers and the open intervals on which the function is increasing or decreasing.…

A:

Q: Two sets A and B are defined as follows: A = {x, y, z); B = {1, 2, 3}. Ug Oh f range of g range of h…

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Q: 2 xy dy + 4y dx = 8 x dx 2 2

A:

Q: -3x If h (x) = ln(x + 4 + e−³ª), then h′ (0) =? 01/10 O nonexistent 0 210 210

A: This is question of differentiationHere function given We have to differentiate it and put value…

Q: 4. COS V sin v = csc v sin v 5. cot(a) cos(-a) + sin(- α) - csc (α)

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Q: Solve the second order. Dieg - Ý - ý syes 1 39

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Q: Find the solution of the following problem. y' - (x + y)(x + y +3) = 1

A:

Q: For which value of t does the line given by the parametric equations x=t-1, y = 1+ 2t, z = 3-t pass…

A: x=t-1y=1+2tz=3-tPoint (-2,-1,4)

Q: For which values of x are the vectors (2x, 4, x) and (-1, -2, x) orthogonal? Select one: O None of…

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Q: Find the absolute extrema (max and min) of f(x,y)=3x^2-2y^2 over the disc x^2+y^2<=1. Indicate all…

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Q: The parametric equations and parameter intervals for the motion of a particle in the xy-plane are…

A: Consider the parametric equation

Q: Let f(x) = 2x + 3 and g(x) = -3x - 6. Compute the following. (a) (fog)(x) (b) (fog)(9) (c) (gof)(x)…

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Q: Does the series below converge or diverge? If it converges, find its sum. Either way, justify your…

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Q: In 1994, the moose population in a park was measured to be 4460. By 1997, the population was…

A:

Q: Consider the function f(x) = 2x³ + 3x² - 36x - 54. a. Find the first derivative. f'(x) = b. List any…

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Q: 7. 8. 9. sect cos t sect 1+sec²x tan*x+1 sin t csc t = sin t = cos x + 1 cos t sect = 1

A: Given.

Q: Find f. f(t) f'(t) = t³ + -/-/7₁ t5 t> 0, f(1) = 4

A:

Q: Consider g(t) = 3t+ 6t² - 1 + 6t³+2+¹ Determine the intervals on which g is concave down. g is…

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Q: TO Find the length of the curve y = In (2 sec x) for 0 ≤x≤ xs 6 The arc length of the curve is (Type…

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Q: The magnitude of the vector (5,-2, 3) is √/38. Select one: O True O False

A: Given vector is: Let vector

Q: (a) Find and sketch the domain of the function f(x,y)=√x+2+√√y+3

A: To find and to sketch the domain of the following function.Note: Since the student has posted…

Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

A:

Q: S Write an equation for a line parallel to y y = -4x + 4 and passing through the point (4,-2

A: To find the equation of a line parallel to y=−4x+4 and passing through the point (4, -21), you can…

Q: 4. Use Calculus to graph g(x)=x² + 4x³. Make sure that your graph shows all intercepts, extrema, and…

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Q: Describe the x-values at which f is differentiable. (Enter your answer using interval notation.) X…

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Q: If what are the bounds of integration for the first integral? a= 11 [ f(a)d= = [ f(x) dx + " f dx […

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Q: √3 4 16 (x-7)(x + 9) dx

A: I=∫3416(x−7)(x+9)dx

Q: Find the area of the shaded region. -1.0 -0.5 y 8 6 y=3e 4 2 0.5 (1, 3e) y=3xet² 1.0 1.5 2.0 X +

A:

Q: 3. a. Find the intervals of increase and decrease for the following. y = 2x² - 8x + 1 b. y=x² + 160…

A: A function f (x) increases in the interval I if f'(x) &gt; 0 for all x in I.A function f (x)…

Q: Let h(x) = 6x² +1+17x Determine the critical values of h. If multiple such values exist, enter the…

A: Given, .For find critical valuer put h'(x)=0.

Q: Set up an integral for the area of the shaded region. Evaluate the integral to find the area of the…

A: The given graph

Q: Sketch the region enclosed by y = 7x and y = 8x². Decide whether to integrate with respect to x or…

A: In this question, we will find the area of the region.

Q: Q/ solve equations 1- y' = ky 2-x(1+y²) dx =y(1+x²) d;

A:

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: r=6cos⁡(θ),θ=π3

Q: Consider the function f(x) : = m2 – 52+4 x + 2 a. Find the first derivative. f'(x) = b. List any…

A: Note:-Since you asked multiple sub parts questions, according to our policy we can solve only first…