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Q: I need help on both. They are both short so please help me on both

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any ...

Q: Evaluate the function f(x) = x+4x +3 at the given values of the independent variable and simplify. a...

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Q: Divide (6x3 + 13x2 - 11x - 15)/(3x2 - x - 3)using long division. State the quotient,q(x), and the re...

A: Given Using long division Divide (6x3 + 13x2 - 11x - 15)/(3x2 - x - 3) To find the quotient, q(x), a...

Q: Find the limit of the following trigonometric function. Show solution.

A: Given: limx→0cosxtanxx

Q: Let C be the positively oriented circle x2 +y2 =1. Use Green's Theorem to evaluate the line integral...

A: The given circle C is  x2 + y2 = 1 Heree the centre of the circle is (0, 0) Radius of the circle r =...

Q: Find the following limit. t2 + 5t – 36 t – 4 lim t+4

A: First, we have to find the limit limt→43t2-1t-5. limt→43t2-1t-5=3(4)2-1(4)-5=48-4-5=39 Now, find the...

Q: -30 dr 1'V + 25 aluate the integral: Which trig substitution is correct for this integral? Oz = 25 t...

A: Solution: The objective is to evaluate the integral

Q: Use a half-angle formula to find the exact value of the expression sin 15°

A: Our Aim is to find the exact value of the expression sin (15°).

Q: Find the derivative. Ignore the boxes

A: Given that y=x+4x2+13 Simplifying we get y=x+43x2+132  

Q: Find the radian measure of the central angle of a circle of radius r =1 meter that intercepts an arc...

A: Given radius r = 1 meter and arc length = 600 centimeters. Angle θ=Arc lengthradius.

Q: 2 - 3x - f 2x-2,

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Q: Write the sum without sigma notation. Then evaluate. 3 :+2 (-1)*2 sin kr k=1 Write the sum without s...

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Q: 10 – x – x2 if x 4 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim f...

A: Given that fx=10-x-x2if x≤42x-5ifx>4   (1) Find limx→4-fx Left hand limit: For x<4 , fx=10-x-x...

Q: Find each limit, if it exists.

A: (a) limx→∞ 3-2x3x3-1=limx→∞ x3x-2x3x2-1x=limx→∞ 3x-23x2-1x=0-2∞-0=0 Thus, limx→∞ 3-2x3x3-1=0.

Q: Use interval notation to represent all values of x satisfying the given condition. y = 2x - 11 + 3(x...

A: Use interval notation to represent all values of x satisfying the given condition. y = 2x - 11 + 3(x...

Q: Show that the function is differentiable by finding values of ε1 and ε2 as designated in the definit...

A: Given function is fx,y=x2+y2. ∆z=fx+∆x,y+∆y-fx,y=x+∆x2-y+∆y2-x2-y2=x2+∆x2+2x∆x+y2+∆y2+2y∆y-x2-y2=∆x2...

Q: Determine whether the given relation is a function. Give the domain and range for each relation. (se...

A: The domain of a function is the set of all possible inputs for the function. Here, the input value i...

Q: 1) solve 3x^2 +2x+5=0 2) solve 8x^2 +14x+9=0 3) solve x^2-2x+2=0 4) solve x^2 +6x+10=0 5) solve 4x^2...

A: As per our guide lines we need to solve only one question.please,repost the remaining questions as o...

Q: Solve and compute Jacobians Solve the following relation for x and y, and compute the Jacobian J(u, ...

A:   Given that,  u = 2x - 3y,  ν = y - x Differentiating partially  with respect to x and y ∂u∂x = 2∂u...

Q: Simplify:[(1 +1/x)/(1 -1/x)]

A:

Q: Find critical number of f(x) = x^2 - 6x + 8

A: To find critical number of f(x) = x^2 - 6x + 8

Q: In Exercises 19-40, calculate the derivative.

A: Given the function f(x)=ex(x2+1)(x+4). We need to calculate the derivative of the above function.  

Q: The first term of a geometric progression is 12 and the fifth term is 55. Determine the 8th and the ...

A: Given information: The first term of a geometric progression is 12 and the fifth term is 55. Concept...

Q: Find the slope of the line passing through the pair of points: (-3, -1) and (-2, 4).

A: We have to find the slope of line passing through the pair of points: -3, -1 and -2, 4 We know if an...

Q: Express the function h(x) = (x2 + 2x - 1)4 as a composition of two functions f and g so that h(x) = ...

A: To express  function h(x) = (x2 + 2x - 1)4 as a composition of two functions f and g so that h(x) = ...

Q: Show that sec x = (sin x / cos x) + (cos x / 1 + sin x), then use the identity to drive the basic in...

A: (i) RHS=sinxcosx+cosx1+sinx=sinx1+sinx+cos2xcosx1+sinx=sinx+sin2x+cos2xcosx1+sinx=sinx+1cosx1+sinx=1...

Q: A positive number is written in scientific notation when it is expressed in the form a x 10n, where ...

A: we have to fill in the blanks A positive number is written in scientific notation when it is express...

Q: Given that sĩn = %3D 2 |cos 플 호 and COS %3D sin = cos 4 = show without Ee using a calculator that co...

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Q: A chemist needs to mix a solution that is 34% silver nitrate with one that is 4% silver nitrate to o...

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Q: Find the area of the region enclosed by the curves y-5x 1 and x-y31. The area of the region enclosed...

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Q: Pls help

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Q: If sin θ = 4/5 and θ lies in quadrant II, find the exact value of tan 2θ.

A: Given:sinθ=45tan 2θ=?

Q: Ssin'x cosde 3. Sin'x cos dx

A: Given: ∫ sin3(x)  cos(x) dx We have to evaluate the given integral.  

Q: sin x Show that secx = cosx - then use the identity to derive the basic integration rule f secx dx =...

A: RHS=sinxcosx+cosx1+sinx=sinx1+sinx+cos2xcosx1+sinx=sinx+sin2x+cos2xcosx1+sinx=sinx+1cosx1+sinx=1cosx...

Q: QUESTION 6 Find the slope of the line that goes through the given points. (7, -8), (18, -18) O 10 10...

A: Here two points are given and we need to find slope 

Q: Given y=square root x , y=3 and x=0. Sketch the region enclosed by the given curves and using the sk...

A: The given curves are, y=x,y=3,x=0. Sketch the given curves and obtain the common region.

Q: If f (3) = 5 and lim,-3 f(x) = 5, then f is continuous at 3. True O False

A: Given data is : f3=5 and limx→3f3=5 A function fx is said to be continuous at x=a if and only fa=lim...

Q: Answer parts A,B and C.

A: (a) Determine the slope dy/dx at different points of the graph. At −1,3,dydx=xy−14=−1×3−14=−24dydx−1...

Q: 3. If you ride the "Drop Zone" at Canada's Wonderland, you will fall toward the ground at speeds in ...

A: Given:

Q: The rate of change of annual U.S. factory sales (in billions of dollars per year) of a certain class...

A: Change of rate in sales per year   S(t)=0.12t2-1.01t+5.7 billionsyearsales every year is given bysal...

Q: Let f(z) = 10z + 6 %3D f (z) = Submit Question

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Q: I need help with this question

A: It is given that, H(x)=∫ex11+t2dt we have to find the equation of tangent line on curve y=H(x) at x=...

Q: Find a plane containing the point (-6,-5,2) and the line ¯r(t)=<4,−7,5>+t<1,5,−5>r¯(t)=&...

A: Given: A plane is passing through the point -6, -5, 2 and contains the line r→t=<4, -7, 5>+t&...

Q: 8. Write the following product of cosines as a sum: 2 7x cos(플), cos을. 3x COS cos(2x) cos(5x) cos(2x...

A: Consider the product of cosines 2cos 7x2cos 3x2. Write the product as sum. Apply Trigonometric Ident...

Q: Verify the ff. identities: cot 0 – sin 0 sec 0 6. - cos? 0 – sin? 0 %3| - sec 0 csc 6

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Q: x° + 4x? dx (a) x² + 4x + 3

A: Due to our guidelines I am solving only first problem please repost other question. I = ∫x3+4x2x2+4x...

Q: Evaluate the integrals ∫2 cot πx dx

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Q: Find the value of each variable. 44 30° y =Dand y= %3D (Simplify your answers. Type exact answers, u...

A: The given triangle is:

Q: find the equatin A the Line

A: The coordinates of the point on the line is -5, 9 and -3, -7.

Q: Prove the inequality V1+æ – 1 –+ < 6 on [0, 0). 8

A: Consider the given inequality in the given interval. Use the graphical approach to prove the inequal...

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.