Which of the following can the first derivative not be used to determine? 1. where the function is increasing or decreasing 2. Concavity 3. Critical Numbers 4. local maxima or local minima

Q: Identify the surfaces of the following equations by converting them into equations in the Cartesian…

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Q: Find the volume of the solid generated by revolving around the y- axis, the region bounded by 1 y =…

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Q: II. Evaluate the following integrals. fe (sin³x)√1 + cos x dx 2.

A: ∫π/2πsin3x1+cosxdx sin3x=sinx(sin2x)=sinx(1-cos2x) ∫π/2π(1-cos2x)(1+cosx)sinxdx let 1+cosx=t…

Q: 3x(xy − 2)dx + (x³ + 2y)dy = 0; f(1)=2 Find the positive root of y at x=2. Use 2 decimal places.…

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Q: Q3/ Using shifting and reflection to draw the following functions. 2- y = √1 ex 2- y = sin(x) + 1

A: As per bartleby guidelines we only give first question answers.

Q: IV. A small business determined that the price-demand and cost functions for producing and selling x…

A: This question is related to profit and cost functions, we will solve it using given information.

Q: Evaluate the following limits 1. lim (2x+x) x → +00 e2x +In x

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Q: 3.2.2 Test for exactness then solve. y(2xy2 − 3)dx

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Q: Daniel saved $260 at the end of every month for 4 years in his bank account that earned 5.60%…

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Q: Find the are a of the region bounded by the given 1) sketch the area, ii) Determine the boundaries a…

A: This question can be solved using the concept of area under curves.

Q: Volume of Solid of Revolution Submit a pdf file of your handwritten solutions to the problem.…

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Q: Evaluate the following integrals S- 3 • │e* − e| + (e* + = e) + e) dx e 0

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Q: II. Evaluate the following integrals. 1. 1 - coth² (log₂x) x cosh (log₂ x) -dx

A: The integration of the integral is;  [1-coth2(log2x) ]/[x cosh(log2x) ].

Q: Given the function f(x) √x f(x) = COS 2 1 + √r dr Determine the instantaneous rate of change at x =…

A: Using Leibniz rule of derivative

Q: Evaluate the following: 4 fsin 2xcos²2xdx

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Q: Is that pi (π)? Or something?

A: Given ,  Area of the region bounded by  y = cosx , x = -π/2 and x = π/2 and the x - axis  We have to…

Q: Evaluate the indefinite integral given below using the indicated substitution. /-20 -2(-2x +9)³ dx u…

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Q: Graph the problem and solve using vertical or horizontal rectangle. Show your solution. 1. Find the…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: x² Define R as the region bounded by the graphs of f(x) = 2√x and g(x) = over the interval [0, 1].…

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Q: 1. Use local linear approximation to estimate In (0.99). 2. Find the absolute extremum values of…

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Q: !

A: Please refer to the image below

Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^3, y-axis,…

A: The region is bounded by y=x^3, y axis  and y=8.And the region is revolved about x=0. We need to…

Q: Find the area (in square units) bounded by the parabolas x² + 2y - 8 = 0. a. 7.10 sq. units b. 7.01…

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Q: The following differential equation is a Bernoulli equation: 2 dy = y³ where y = f(t) dt t By making…

A: To convert into linear differential equation.

Q: If F(x) = = [₂√₂ x² a. F'(1) b. F(2), by interpreting F(2) as an area √4t - t² dt, evaluate the…

A: Given: F(x)=∫x20 4t−t2dt To find : F'(1) and F(2)

Q: = t² - 6t + 8, The velocity function of a particle moving along a horizontal line is given by v(t)…

A: Velocity and acceleration

Q: The pedals of a bicycle are mounted on a bracket with centre 27.5 cm above ground. Each pedal is…

A: 1) Center = 27.5 cm  Radius = 17.5 cm  Rate = 10 cycles per minute => Rate (ω) = 1/6…

Q: 5. Simplify: y23 x7 O x7 y ¹5 15 x7 y15 O x7 y 2³ (x5)-2 x ¹ y ² 3 xy-3 (y-6) ³

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Q: In x 2. Use a local linear approximation of f(x) = 1+x² to estimate In (0.9) 1.81

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Q: Evaluate ¹ dx √√9-4x2 a. 0.285 b. 0.123 c. 0.423 d. 0.365 e. NONE OF THE ABOVE

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Q: II. Evaluate the following integrals. 1 - coth² (log₂x) dx rcosh (log₂x) 1. S

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Q: Find the area of the region bounded by the curves y = the x-axis using vertical strip. (x+1)2 y = 4…

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Q: Electric usage over the course of a day varies. The graph shown is of electricity costs per hour.…

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Q: 64 1 (c) Ltd (√t - 1 - / t + √²) de dt √t (d) * (sin(2x) + cos(2x)) da 0

A: To evaluate the following definite integrals using the Fundamental Theorem of Calculus.c ∫164t-1t+t3…

Q: 3. A particle is moving along a horizontal line such that its velocity in m/s is given by v(t) = 2t²…

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Q: lim x→0 sinh x2 – x2 sinhx−x

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Q: While buying a new car, David made a d payment of $1,100 and agreed to make end payments of $230 for…

A: Please refer to the image below

Q: √ x-1 x² + 5x +8 dx

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: II. 3 4. 5- 10² - 0 + (0² + 0) dx S le* -e (e* e) e 0 Evaluate the followin

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Q: A curve with polar equation r = represents a line. Write this line in the given Cartesian form. y =…

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Q: Determine the values of r for which the differential equation y" +9y' + 20y = 0 has solutions of the…

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Q: Evaluate the indefinite integral given below. Provide your answer below: f6e4 tan (2x) sec² (2x) dx…

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Q: Electric usage over the course of a day varies. The graph shown is of electricity costs per hour.…

A: Use average concept

Q: 2. lim (tanx) (sin r-1) x→

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Q: . Calc.   Test for exactness then solve. (2xy - sinx)dx + (x2 - cosy)dy =0

A: Differential equation

Q: 5. Find the volume of the solid generated by revolving the region bounded by y = e-x², the x-axis,…

A: Solution given below

Q: 2. Evaluate the integral: SSS teu du ds dt

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Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

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Q: 4x Find the average value of the function f(x): - 5 Submit your answer as an exact value. Provide…

A: Given problem:- Find the average value of the function f(x) =(4x/5) + 1 over the interval [-1,3].

Q: Definition of first order, explicit ODE and the definition of it s solution.

A: Solution