differential equation dy/dx= 2^-x at the indicated point

Q: Evaluate the limit sin 8x lim x 0 sin 2x

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Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.…

A: Given function f( x ) = 36-x2

Q: You are planning to make an open rectangular box from a 38-in.-by-75-in. piece of cardboard by…

A: This question is based on application of derivative. First take a square of length x then make a box…

Q: 3. Use the Gizmo to experiment with more functions of the form y = b*. Select the Show probe and…

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Q: nf is shown. f'(x) 6 X nter your answer using interval notation.) Enter your answer using interval…

A: We have to find the intervals such that function is increasing and decreasing according to the given…

Q: Express the integrand as a sum of partial fractions and then evaluate the integral. 10x² - 1 S 4 X X…

A: Given integral : ∫-10x2x4-1dx To find: The value of given integral using partial fraction. Let I =…

Q: The integral gives the area of the region in the xy-plane. Sketch the region, label each bounding…

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Q: 10x3-8x4+2x3 2 2 X→0 15x4+3x3-5x Evaluate Lim

A: We need to find the given limit limx→010x43-8x34+2x2315x24+3x23-5x

Q: [4-R] [CLO 15] Let f : R → Rx ↦ x2. That is,  is defined by the formula f (x) =x2. Give a formula…

A: The given function is: fx=x2

Q: The equation of motion of a particle is s = t³ - 12t, where s is measured in meters and it is in…

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Q: Use logarithmic differentiation to find the derivative of the function. y'(x) = X-3 x + 3

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Q: -1 If ƒ(x) is a positive 1-1 function with inverse ƒ−¹(x) with f(a) = c and ƒ(b) = d then d π ñ ["°*…

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Q: Answer the following questions. 1 A function f is given by f(x) = (x+1)|x+3| x+3 (a) Express f(x)…

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Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: Use the theorem given below to find the curvature of r(t) = √62²i + 2tj + 2t³ k. k(t) = Theorem: The…

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Q: You are designing a 1152 cm³ right circular cylindrical can whose manufacture will take waste into…

A: We use the differentiation method to find the required ratio

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

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Q: Consider the function f(x) = 4 2 x² x7 Let F(x) be the antiderivative of f(x) with F(1) = 0. Then…

A: Topic = Integration

Q: Find the value of x on the graph of y = x² where the slope is 16. (a) 4 (b)-4 (c) 2 (d) 8

A: To find the value of x on the graph of y=x2 where the slope is 16.

Q: Determine the x-intercept of the plane: [x, y, z]= [3, 1, 3]+[1, 1, -1]+[0, 1, 3]

A: Question -   Determine the X intercept of the plane

Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.…

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Q: Consider the following. x = ln(t), y = 2t, z = t², (0, 2, 1) Find the equation of the normal plane…

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Q: x ». Let g(t) be the function whose graph is given below. Let G(x) = g(t) dt, 0 ≤ x ≤ 5. Where does…

A: Given: Gx = ∫0xg(t)dt   , 0≤x≤5 To find: The point of maximum and minimum of G(x) and maximum ,…

Q: Find the particular solution to the given differential equation that satisfies the given conditions.…

A: Given differential equation:- x2+y28dy=7xdx+ydy

Q: Differentiate the function. f'(x) = f(x) = In(cos(x))

A: The solution is shown below-

Q: Use logarithmic differentiation to find the derivative of the function. y'(x) = y=(√x)⁹x

A: The given function is: y=x9x

Q: Find a formula for the n" partial sum of the series 5- th The formula for the nth partial sum, s of…

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Q: 4sqrt(2) was incorrect

A: Given:= f(x,y) = x3y2U = (-3,3) P= (-1,-2)   The directional derivative being negative means that…

Q: Q13 Use the limit definition of the derivative to find the derivative of the following function:…

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Q: Find f'(x) and simplify. X x + 36 f(x) = Which of the following shows the correct application of the…

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Q: (a) Find the derivative. y = In(4x - dy dx (b) Find the derivative. y = ln ( 4x = dy dx 6) - 3 In(x)…

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Q: Evaluate the limit using L'Hospital's rule if necessary x 5 7 lim (1+1)

A: To find the limit

Q: Find the values of x, y and z that correspond to the critical point of the function f(x, y) = 3x² +…

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Q: Q11 Compute (a) [3.14] = dx (b) Compute [54] = d 5-4x- dx 3

A: To compute the following. (a) ddx3.14 (b) ddx5-4x3

Q: Let a = (5, 1, 0) and b = (2, – 4, − 1).

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Q: Determine if the function f(x) = r²-3x+2 satisfies the hypotheses of the Mean Value Theorem (MVT) on…

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Q: Find the future value of the following ordinary annuity. Payments are made and interest is…

A: Given : Find the future value of the following ordinary annuity. Payments are made and interest is…

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.…

A: We need to change the integral into polar integral ∫0ln6∫0ln62-y2ex2+y2dxdy

Q: d. f(x) = 3x4. 3x²-2 2x

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Q: Question 16 ( Find the slope of this line. Part 2- Full solution problems. A line with positive…

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Q: Find the relative maxima and relative minima, if any, of the function. (If an answer does not exist,…

A: We find the first and second derivatives using the power rule F(t)=3t5-20t3+20F'(t)=ddt3t5-20t3+20…

Q: Use spherical coordinates. Evaluate III z dv, where E lies between the spheres x² + y² + z² = 4 and…

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Q: Ifis decreasing and its graph is concave pon (0, 1), which of the following could be graph of the…

A: If f is decreasing and its graph is concave up on (0, 1). Wich of the following is the graph of f'…

Q: (a) Use differentiation to find a power series representation for 1 (6 + x)2 f(x) = f(x): 00 Σ n = 0…

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Q: The derivative of a function is given f'(z) = (2²-21-8)g(x) for some unspecified function g such…

A: The first derivative of a function is given by fx = x2-2x-8gx,   gx>0 To determine: The point…

Q: Consider the following scenario. Suppose you start at the point (0, 0, 8) at t = 0 and move 10 units…

A: Note : We have to solve gien sub parts.

Q: Question 2. Consider the following linear programming problem. Min 7.505 + 9.00P s.t. 0.105 0.065 5.…

A: NOTE: Refresh your page if you can't see any equations. . for simplicity use the variables S=x and…

Q: Given f(x, y) = 100x + 80y - 2x²- 4y² - xy Evaluate f(10, 9)

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 2 Find the volume of the solid obtained by rotating the region bounded by y = x² , y = 0, and x = 3,…

A: we have to find the volume abouts y-axis

Q: Express the given integrand as a sum of partial fractions, then evaluate the integrals. 1 1 y+2 2…

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