PART I: Write an expression that is complex enough to be differentiated using the: Product Rule Chain Rule PART II: Answer to the derivative problem: f(x) = (7x3 + 5x)(5x-12)2

Q: Find the sum of all the odd numbers between

A: Given,            Sum of all odd numbers between 21 and 355 inclusive.To find : Find the sum.We know…

Q: Find an approximation of the area of the region t under the graph of f by computing the Riemann sum…

A: We have to find the area.

Q: 4. (- FIND the center of mass of the lamina of density p if the lamina is shaped like the region…

A: A detailed solution is given below.

Q: Consider the equation cos(3t) = 0.8. Find the smallest positive solution in radians and round your…

A: We can find the answer the as below.

Q: For what values of x does the series converge conditionally? 5x Σ n! n=1 1 O A. x= -7 5 OB. X=0 1…

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Q: Find the center of x 2 + y 2 - 10x - 8y + 1 = 0. (5, 4) (-5, -4) (-10, -8)

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Q: Find T(t) and N(t) at the given point. r(t) = 8 cos(t)i + 8 sin(t)j; t = 1|3

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Q: Find the minimum value of f (x,y,z) = 2x² + y² + 3z² subject to the constraint 2x - 3y - 4z = 49

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Q: Use the table to evaluate the expression. 1 2 3 4 f(x) g(x) 3 1 6 3 4. (g o f)(2)

A: Here (g∘f)(2)=g(f(2))But f(2)=3(g∘f)(2)=g(3)and g(3)=6Therefore(g∘f)(2)=6

Q: Q1// Find the Area bounded by: x = -y2 and x = y-2

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Q: A radio transmission tower is 211 feet tall. A guy wire is to be attached 6 feet from the top and is…

A: We have to solve above question and find length of wire As per bartleby guidelines we have to solve…

Q: Find dy/dx: 1. у %3D Vu du

A: Given: y=∫0t4udu

Q: What are all values ofk for which x'dx = 0?

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Q: Find the exact length of the polar curve. r = e4?,    0 ≤ ? ≤ 2?

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Q: Given two vectors u and v that form an angle of 60° (when joined tail to tail) and given that | V| =…

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Q: Find the area of the region bounded by the graphs of the equations. y = -x² + 6x, y = 0

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Q: 8. If F(x)= dt, then F'(x)=

A: Using Leibnitz rule for integral.

Q: 3. Find the equation of the final function after all the following transformations have been made on…

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Q: An open box of maximum volume is to be made from a square piece of material, s- 12 inches on a side,…

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Q: gas is escaping a spherical ballon at the rate of 4cm per minute . how fast is the surface area…

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Q: Evaluate y' of the given functions: (х-4) y = x2

A: Here is the solution:

Q: Find the eccentricity of 8x 2 + 6y 2 - 32x + 24y + 8 = 0. 2 1/2 2√7

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Q: The amount of garbe, G produced by a city with population p is given by G = per week, andp is…

A: As per our guidelines, we can help you in solving only first problem, rest of the problems you have…

Q: x2 – 3x – 2 if x 4 f (x) = - (2x + 1

A:

Q: Consider the polar equation defined by r = 5 cos(2 sin 6), where 0<0< 27. Determine the missing…

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Q: 6. During the worst 4-hr period of a hurricane the wind velocity in miles per hour is given by v =…

A: The average value of the function is given by;0≤t≤4v(t)=1b-a ∫abv(t) dt     =14 ∫04(5t-t2+100) dt

Q: For a, b E R, calculate (ax + b)dx (x²+1)²(x²+4)*

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Q: State the condition that the two vectors i and y are perpendicular. Find the value(s) of k such that…

A: If two vectors are perpendicular to each other, then their dot product is equal to zero.

Q: Find the sum A+B+C of the constants A,B and C appearing in the Taylor series expansion given below:…

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Q: Show that whether x5 + 10x3 + x + 1 is O(x4) or not?

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Q: Determine the direction vector of the following lines where lz is in 3D a) l1:2x – 3y + 6 = 0 %3D -…

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Q: 5. The velocity function of a moving particle on a coordinate line is v (t) = t³ + 6t² + 11t + 6.…

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: Area: 7A square centimeters

A: The length is 7/3 cm and breadth is 3 cm or vice-versa for the perimeter to be minimum

Q: Find an equation of the line tangent to the curve r = sin 30 at the point where 0 =

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Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: Find the Taylor series generated by fat x = a. 1 f(x)=, a=9

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Q: 3. Find the area bounded by a curve y? = 6x + 36 and the y - axis 4. Find. the area bounded by y =…

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Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

A: Let's find.

Q: 1 x + ex 2 g dx

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Q: Find each limit, if it exists. xA + 4 (a) lim x- 00 x4 - 3 (b) lim *+ 4 x- 00 x - 3 (c) x4 + 4 lim

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Q: 4. The function A(t) = 2000(1.)' represents the growth of algae in a pound after time t (in hours).…

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Q: Find the volume of a solid bounded by y=(x2 -4) and y=(2x - x2) about the axis y=-4.

A: formula : here

Q: Given the two vectors: å = 2ỉ -j+k, b = i + 2k and d = 3ỉ + 5j in 3D. a) Determine the dot product…

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Q: 2. Use the graph below of y = f(x) to answer the following question. point 8 4. point 1 point 2 3 2.…

A: To answer the given function using the given graph.

Q: Determine the indefinite integral 4 √√x + 3 6x 1/0² - 1717 dx 4 X

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Q: Find the area under the graph of the function y=2-x-x² over the interval [-2,1].

A: Given query is to find the area under the curve.

Q: Find the first 6 nonzero terms of the general series solution of the differential equation…

A: We have to find the general solution of the given differential equation.

Q: h2 Evaluate the follawingcartesian integrat by changing them inte equivalent Pelar integrals: dy dx…

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Q: 8. Determine if 2n-1 [5 -1 is cont 7n n=1

A: Given

Q: Consider the following rectangular box. F a) Give a pair of equal vectors. b) Give a pair of…

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