Problem 1. Draw a direction field for the given differential equation. By hand, sketch an approxi- mate solution curve passing through each of the given points. dy dr (0) » (-;) - 2. = 2, (b) y | = 0

Q: Use the Quotient Rule to find the derivative of the function. 3x - 7 g(x) = %3D x² - 1

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Q: 5 can

A: We will find the time period. 

Q: Prove the following identities. cos( - ) sin x/2 sin x sec x/2

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Q: Evaluate the integral using trigonometric substitution. 1 dx xV1 + x6

A: Given ∫1xx6+1 dx Substitute u =  x6 + 1→dudx=3x5x6+1→dx=x6+13x5 du =13∫1u2-1 du Now solving ∫1u2-1 d...

Q: A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 8 ft above the bo...

A: Note: Since you have asked part b, we will solve only part b. 

Q: A graphing calculator is recommended. Consider the following. cos(x) = x3 (a) Prove that the equatio...

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Q: y In(x) ln(y)dx + dy

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Q: 3. Evaluate: e-x²+2x dx (Hint: let t = (x – 1)²) %3|

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Q: Write an equation for a rational function with: Vertical asymptotes at x = -6 and x = -2 x-intercept...

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Q: cos“ I dr 4 sin* I

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Q: mine where the function is concave upward and where it is concave downward. (Enter your answers usin...

A: Given query is to find when function is concave up and when concave down.  

Q: Find the unit vector having the same direction as v = (1, - 3). %3D 1 3. V 10 V10 10 V10, 3. O (1, 1...

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Q: What are the roots of the auxiliary equation corresponding to the DE y" + 3y" + 3y' + y = 0? Write t...

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Q: (x+2)? Consider the ellipse whose equation is given by + (y+ 5)2 = 1. 25 What are the coordinates of...

A: Coordinates of vertices are:-

Q: n hired at a new job selling jewelry, you are given two pay options: on A: Base salary of $15,000 a ...

A: Given query is to find the amount of sale so the option A will be batter 

Q: Integrate the following functions: 1. S sin 2x dx

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Q: The Heaviside function is used in engineering applications to model flipping a switch. It is defined...

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Q: 2. S(Vw +2)Vwdx

A: Topic:- integration

Q: 6. If f is continuous and f(x)dx=4 , '3 | xf(x?)dx=

A: Explained below 

Q: Question Select your answer. A certain radioactive element decays according to the ()' 39.60 formula...

A: Given  :initial No=5000 gramsR(t)=No12t25limt→175R(t)

Q: (MULTIPLE CHOICE) Which of the following equations is(are) variable separable? dN + N = dt N dr (A) ...

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Q: A rectangle has an area of 198 cm and a perimeter of 58 cm. What are its dimensions? Its length is I...

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Q: Evaluate f tan²xsec*xdx using trigonometric integrals

A: Our Aim is to evaluate the integral given below:-∫tan2 (x) sec4 (x) dx -(i)

Q: For the next six questions, consider the differential equation: y/" + 4y = g(x), g(x) # 0

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Q: 2. Let r+1 I <-1 f(x) = { 2– Vr² + 7 [3r – 4] r 2-1 Determine if lim f(x) exists. r+-1

A: Find left and right hand limit and using L hospital rule. (Indeterminate form)  Since left and right...

Q: 1)) The point H(2, 6) is reflected over the x-axis. What are the coordinates of the resulting point,...

A: The given point H(2, 6)

Q: Iz + 기 b. lim x+ 8 ² +7x - 8) I-8-

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Q: Determine the standard form of equation of a hyperbola with vertices at (2,3), (2, – 3) and passing ...

A: Given problem:- Determine the standard form of equation of a hyperbola with vertices at (2,3), (2, -...

Q: 15 1야 -5 10 /15 -20 -15 -10 20 -5 -10 -150 -20 lim f(x) x--5 -5 lim f(x) 10

A: Topic = limits

Q: Simplify (129 + 121 + i) (12021)

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you wa...

Q: 44. Write the complementary function for the given DE.

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

Q: I'y" The expression log| z18 can be written in the form A log(x) + Blog(y) + C log(z) where A = B = ...

A: We can find the answer i.e the value of  A, B &amp; c  as below.

Q: |r+7| 9. b. lim r-8- x2 + 7x -8, x + 8

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Q: - 1. der the equation In ay Ehow that (r, y) = (1,1) is a solution to this equation. dy Find dz (my)...

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Q: A box with a square base and no top is to be made from a square piece of carboard by cutting 5 in. s...

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Q: Find the derivative of the function. h(t) = (t5- 1)(312-5t-2) %3D

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Q: get

A: We will find the rate of change of value. 

Q: -1 | tan *xdx

A: The given integral,       ∫tan-1x dx

Q: Write an equation (any form) for the quadratic graphed below: 4- 2- -5 -4 3 -2 -1

A: Vertex =(h,k)=(2,1)From graph ,Parabola passes through points :(0,-1) &amp;(4,-1)std equation of par...

Q: O XsinCyldx +(x^t)cos(y) dy=0

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Q: 1. Evaluate the following limits. x+ Vr - 3r а. lim Vr4 + 3x

A: We have to find limit

Q: | cot?xcsc?x dx х ах

A: We can find the integral answer as below.

Q: Find the radius of convergence and the interval of convergence. k2 + 81 k=1 Radius of convergence: I...

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Q: r (t) = -li+ (9 cos(t)) j+ (9 sin(t)) k

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Q: (MULTIPLE CHOICE) Which of the following is(are) differential equation (s) with homogeneous coeffici...

A: To determine which of the following is(are) differential equation(s) with homogeneous coefficients.A...

Q: Find a formula for the graph in terms of f (x) = sin x or g(x) 10 = COS X. NOTE: Eter your answer in...

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Q: 13. Find the solution set of e) 2x? – 3x – 4|<5

A: Given query is to find the solution of the expression.

Q: fa 4 – 3 cos x) sin² x dx

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Q: 4x+2 find average rate of change from x=-1 t x=1

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Q: Partial Fractions w/ long division first 4.S x4- 2x3 + x2 + 2x – 1 dx x2 – 2x + 1 long division b/c ...

A: Integration