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Q: Evaluate the definite integral. 1 5x +6dx

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Q: Compute the derivative of the given function. f (x) 10x-1/4 cos e + 7 sin a %3D -

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Q: d太 2.

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Q: 7. Use the Method of Lagrange Multiplier to find the critical points of the function f(x, y, z) =…

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Q: 5. Let f be a function satisfying the following properties: continuous on R \ {0} • f(-1) = -3 •…

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Q: (a) How many integers from 200 to 2000 inclusive are multiples of 4?  (b) How many integers from…

A: As per our guidelines we are supposed to answer only three sub parts of the question. So I am…

Q: dx If x2 - 2x – 4 is solved by trigonometric substitution, which of the following substitutions is…

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Q: xy + y² dx dy Find the general solution of

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Given: dx Using trigonometric substitution, solve for the integral form in terms of 0. 0 d® B sin² 0…

A: Given: ∫x2-9x3dx Let I=∫x2-9x3dx   To solve this integral we need to do the trigonometric…

Q: I. Evaluate 4x² + 4x + 5 dx

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Q: The integral 15x* - x* - 43x – 19 (x + 1)2(x2 – 6x + 13) can be rewritten as

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Q: dy Solve for the general solution of the differential equation (ax+by+c)² where a, b, c e R dr and…

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Q: Use polar coordinates to evaluate the integral where R is the region that lies in the second…

A: follow the procedure given below.

Q: 9. Evaluate limf(x) = {"_ (x – 2; x 3 %3D x-3 а. 1 b. -4 с. 3 d. Does not exist 10. Evaluate limf…

A: Our Aim is to evaluate the limit of the expression given below:-limx→3 f(x)=x-2 ; x≤3-4;…

Q: to the South Coast Air Quality Management District, the level of nitrogen dioxide, a brown gas that…

A: Here,  A(t)=0.03t3(t-7)4+60.2, 0≤t≤7

Q: Find the derivative of the function. 5 + 6x - 4/x y% =

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Q: +00 dx II. Evaluate the improper integral x(In x)²

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Q: Vx In 2x dx=u v- v-fvdu Using Integration By Parts, Find Uv- du O 3 xVx In 23 2 12x- dx | O 2 Xx In…

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Q: k! (ii) ek k=1

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: (U.1. 6. Find the dimensions of the closed rectangular box of largest volume with surface area of 16…

A: Surface area of the closed rectangular box:(with square bases) and height h;2x2+4xh…

Q: Find the length of the spiral r = 80 for 0 < 0 < 3. (Use symbolic notation and fractions where…

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Q: 2) Given: f(x) = x+sin(2x) over the interval (0,7) a) Use a sign analysis to find the relative…

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Q: 3. Sin x dx 3- COS

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Q: What change of variables is suggested by an integral containing * V25 + x²? O a tanø O none of the…

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Q: 1 y dydx %3D 0. Select one: O True O False 2.

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Q: Use logarithmic differentiation to find the first derivative. Enter your answer without fractional…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 2 1 lim t++00 \ 5t2 + 6'4t (?, ?)

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Q: Find the derivative of the function y=(4x+1)^5(3x+1)^-4

A: We can find the derivative as below.

Q: x² + y)dx + xy dy = 0

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Q: Find an antiderivative of the function. (a) h(q) = sin(q) H(g) = (b) f(x) = 3eX F(x) =

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Q: Find the point(s) on the graph of f where the tangent line is horizontal. f(«) =x°c* (0, 0), 9, 99…

A: We need to find points where tangent is horizontal.

Q: 4. S Vä(x² + 2) dx 5. S(-3 Vã – 6x v7) dx 6. (9x*-6x²+7x²-5x+15 dx 3x

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Q: 1/2 The result of dx is F(b) – F(a), where F(a) and F(b) are real numbers. What is the value of F…

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Q: Find the points on the ellipse 5x2 + y² = 5 that are farthest away from the point (1, 0). smaller…

A: To find the points on the ellipse 5x2+y2=5, that are farthest away from the point 1, 0.

Q: 3x — 1 - dx (x – 2)(x + 5) 3 In |æ – 2| + In |æ + 5| + C 3 In |æ – 2| + In|æ + 5| + C O A Ов 16…

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Q: ] Let D be the region bounded between x + y = 4 and x + y = 9 that lies within the second and the…

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Q: I = 10+ 2s I - 1 y +3 12 - z Consider the lines defined by the equations ( : and l2: 9. y = 5s z =…

A: We have to find intersection Point of given line and equation of plane which contain both line.

Q: Given: dx x3 Using trigonometric substitution, solve for the integral form in terms of 0.

A: This question can be solved by taking x=3secθ

Q: x² – 9 dx ? Using trigonometric substitution, what is A) none of the choices 1 seç x² - 9 + C (В +…

A: Sec²(t)-tan²(t)=1 Sin²(t)+cos²(t)=1 Sin(2t)= 2sin(t)cos(t) 2sin²(t)= 1-cos(2t)

Q: Integration by Parts Example 4. Evaluate In x dv,

A: The given integral is: I=∫lnxdx   As we know that; ddxlnx=1x

Q: sec(0) Compute the area A bounded by the line r = 7 e and the rays 0 = 0, and 0 = 4 as an integral…

A: Here, the formula used is: A=12∫abr2dθ

Q: Q5/Find the Laplace Transform -3 4- f(t) = V2t E) = va Where r %3D

A: To find the Laplace transform of given function.

Q: 00 Given: (1 + 2x)e*dx̟ Using integration by parts and letting dv 00 is %3D u = -1 - 2x, then the…

A: Let's find.

Q: Find the average rate of change of the function over the given interval. R(0) = 40 +1; [6,12] AR…

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Q: dh _10. A cylindrical piston with fixed radius r = 3 cm is being compressed so that How h =- dt fast…

A: Given

Q: 4 Using Trigonometric Substitution x2 +4x - 5 dx = | f(e)de find the new limits of integration. X+2…

A: By using Trignometric Substitution fin the limits∫14x2+4x-5x+2dx=∫abf(θ)dθ

Q: хdу — ydx — Vx? — у?dx 3D о

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Q: The plane y = 1 intersects the surface z = x° + 5xy – y* in a certain curve. Find the slope of the…

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Q: Determine the speed along a parameterized path s(t) = (9t³, 7t²) at time t = 6 (assume units of…

A: Given problem Determine the speed along a parameterized path s(t) = (9t3 , 7t2 ) at time t = 6…

Q: 41. Suppose that both f and g have inverses and that h(x) = (f o g)(x) = f(g(x)). Show that h has an…

A: Explanation of the answer is as follows