4: A- Solve the differential equation subjected to the condition y0)=1 dx

Q: please answer number  2 and follow the format of sample solution (include the rules/techniques used)

A: Here we have to find the integral

Q: Select the correct answer. 12 , 30 lim Sn? what is the value of noo If O A. 24 O B. 50 OC. 84 OD. 75

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Q: Evaluate the integral. (Use symbolic notation and fractions where needed. Use C for the arbitrary…

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Q: Parametric Equations. Show complete solutions. 1. Find the equation of the tangent line (s) to the…

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Q: (d) g(x) = v4 – x²;(-2,2) 2 (e) f(x) = (x + 1)3; [-2,1]

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Q: 5. Given y = af(+ 1), Find when x=1 if f(2) = 4 and f'(2) = 5. dx

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Q: 2. Find the area of: (a) the region bounded by y = x^2, the x-axis and the line x = 2 (b) the region…

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Q: What are intervals of concavity of the function f(x) = -2x' + 6x² – 3 ? a. Concave upward on (1, 0)…

A: Here we have to check the concavity of the graph.

Q: (a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (x³ +…

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Q: Sketch the graph of f(x) = –3r³ – 4x² + 6x – 2 by following the steps in sketching the graph of a…

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Q: The integral of the given function f dx is equal to a. 0.116 b. 0.611 с. О.117 d. 0.161 e. None of…

A: Here we have to find the definite integral.

Q: Given the vectors v and u, answer a. through d. below. v= 6i + 2j- 3k u = 3i + 4j a. Find the dot…

A: We can find the dot product as below.

Q: 1 n =1 (2n- 1)4 M8

A: Integral test

Q: Determine the linear approximation of f(x) = x* at x = 1. а. у %3D 4x - 3 O b. y=- 4 x - 3 О с. у-…

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Q: Evaluate the difference quotient for 7x+1. Az) - f(x) = 2 7/2 7 O 1/2 O O

A: Here we have to find the quotient difference of a function.

Q: Write the sequence in closed form. Make sure to indicate the domain. 3 %3D aj = 5

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Q: 1. Find the sum: ( a) Σ (3i-2) (b) Ej-s 70 2 =3 jG-2) (C) Σ25, 2i(i – 1)

A: To find the sum of the given finite series. Note that: ∑i=1n1=n∑i=1ni=n(n+1)2∑i=1ni2=n(n+1)(2n+1)6

Q: How did you get the volume of the hole and the ball? Referring to 4/3pi in the beginning

A: We know volume of a sphere of radius r=43πr3 cubic unit

Q: 5 Gin Ococodo sin 20 + 3rino-4

A: We will find the integral using the method of substitution.

Q: Consider the function f(x) = x2-1 (a) Find the intercepts of the graph of f (if any). (b) Find the…

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Q: A garden lot is bounded by the curves y = x and y = 9. If its area is in square meters and it will…

A: We will find the area and cost.

Q: b) f(x) = x2-x %3D x²-1

A: To find out where the function is discontinous.

Q: (5) Suppose m and bare constants. What is the linearization of the function f(x) = mx +b at any…

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Q: 6. If z2 = x2y2 (where x, y, and z are positive), and dz then what is when x = 2 and y = 3, given…

A: Given problem:- If z2 = x2 y2 (where x, y, and z are positive), and dz/dt then what is when x = 2…

Q: Select one: O True

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Q: Calculate the value of (1+2i)² and then use this value to find the roots of z-z+ (1 – i)= 0. (1+…

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Q: Determine whether the function has a limiting value. Find the limiting value if it exists.  f(x) =…

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Q: а. 4(е?) b. 4(e² – e*) с. 4(e* — е?) d. 4(e*) e. None of the above DA DE D.

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Q: What are intervals of concavity of the function f(x) = -2x' + 6x² – 3 ? O a. Concave upward on (1,…

A: Given query is to find the the interval where function is concave upward and downward.

Q: 7. y = csc csc (3x – 1) 8. y = 3secx + 45

A: Solving

Q: - %3D

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Q: 00 (-1)2n Vn² + 6n n=1

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Q: f(x)=(5+x4)1/4 what is f2(x)

A: Given query is to find the second derivative of the expression.

Q: Hi! I am a bit confused before the third step. How did you go from xsin-1y to 1-ln(xy)? Can you…

A: Given

Q: 1 Verify that tan?(csc-1(x)) = x2 – 1

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Q: 8. For the function f(x) = x2 - 2, find: a) The slope of a tangent line at x = a.

A: To find the slope of tangent line at x=a.

Q: The series 7 n3+ 9 n=1 6 n+ 1 is divergent. Select one: O True O False

A: Given query is to find that statement is true or false.

Q: Given the ordered pair P, determine the requested sin, cos, or tan of angle a. P(5,5) tane = %3D -1…

A: Given query is to find the value of the indicated function.

Q: In the last 4 line, where is the ^2 in the ln part?

A: The given integral,      ∫13arctanx dx

Q: -2 is a critical number of the function f(x) = 2x - x2. Select one: O True O False

A: Given: f(x)=2x-x2

Q: Using binomial expansion, write down the first three terms of the expression below, starting with…

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Q: What is the area of the enclosed regions in problem number 3?

A: We can solve this as follows:

Q: Using Green's Theorem, evaluate (sin z – y) da + (a³ + e") dy where C'is the circle x2 + y = 4.…

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Q: Express the vector P, P2 in the form v = v,i+ v2j+ V3k if P, is the point (- 8, - 1,8) and P2 is the…

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Q: What are intervals of concavity of the function f(x) = 2x - 6x² – 3 ? Concave upward on (1, o) and…

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Q: Hiw:-boundary Value problems- Q/solve xy-ý=o yco)+ ylo)= 1

A: We have to solve the differential equation.

Q: Use calculus to solve the ff. A particle moves down a horizontal route that begins 5 feet to the…

A: We have to find when the particles will collide

Q: The graph of the derivative y = f'(x) of f(x) is given below. According to the graph, we have f(0) >…

A: We have to tell whether it is true or false

Q: The graphs of the first and second derivatives of a function y = f(x) are given below. According to…

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Q: Which of the following statements is true about the function f(x) = x' - 6x²? a. The graph of f is…

A: We will check second derivative to find concave up and concave down.