Σ (-1)" n=0 2n TT (2n)!

Q: Find the difference quotient x) = 2x² + 3x 2 - f(a+h)-f(a) h where h 0 of

A: Given query is to find the difference quotient.

Q: From 7 consonants and 5 vowels, how many words can be formed consisting of different consonants and…

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Q: The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

A: Let the length of a diagonal is = d1=x m So the length of the other diagonal = d2=(x+2) m. Given…

Q: 9) Find the equation of the tangent to the curve y = 1+ Int and x=t+Int when t = 2.

A: Given problem:- Find the equation of the tangent to the curve y = 1 + lnt and x=t+Int when t = 2 .

Q: 3 1 L₁ dz -3 (x+2) ³0 Compute the integral:

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Q: dw For the functions w= -5x² + y², x = cost, and y = sint, express as a function of t, both by using…

A: Given query is to find the Indicated derivative.

Q: 1. Evaluate the given integral Q. JR (y - 2x) dA, R where R is the region bounded by x = 0, y = x, x…

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Q: s dx 3x²+2x+5

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Q: If repetition is not allowed, in how many ways can we arrange ♣, ♠, ♦, and ♥ a) four at a time? b)…

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Q: Find the inverse of the function on the given domain. f(x) = (x-5)^2, [5,∞) f-1(x) = =

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Q: S 10dz 4z3-4z²+5z

A: To evaluate the given integral:

Q: Use the binomial theorem to expand the expression (u - 5v)¹

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Q: A drag racer accelerates at a(t) = 96 ft/s2. Assume that v(0) = 0 and s(0) = 0. a. Determine the…

A: To find out the distance/position function.

Q: 2. f(x) = x³ senx cos x

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Q: Find the center of the mass of a thin plate of constant density & covering the region bounded by the…

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Q: 5-x Find the family of the curve whose slope at any point is y-3 passes through the point (2.1) and…

A: Topic:- calculus

Q: Find the derivative of the function using implicit differentiation. 1.) x²+y²= 16

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 5. Use the graph to estimate the limits or explain why the limits do not exist. V (a) lim F(x) x-0…

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Q: Find Value of integral ) dx X+1

A: Given query is to find the value of the integral.

Q: . Find the derivative of a composite function using the Chain Rule or General Power Rule. 1.)…

A: As per the company's guidelines, we are supposed to solve first three sub-parts for you, kindly…

Q: 3. A spherical balloon is inflated at a rate of 100 cm3 /sec. How fast is the radius changing when…

A: We know that volume of the balloon is V=43πr3                          (1) Given that Spherical…

Q: əz Let z = x² + y³, x = 2st and y = s-t². Compute for and ar

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Q: Mo Tu We Th Fr Sa Su Date Evaluate the following integrals: (show solution) 1 as √ x²+2 b.) f x+1…

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Q: dw ow For the functions w = xy + yz + xz, x= u + 3v, y = u- 3v, and z = uv, express and using the…

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Q: 1. Is a function f(x)=√x differentiable at a) X = 1 b) X = 0 c) X = -1

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: sec x = Let f(x) + x³e² - log₂ (5x + 1) + 1 x² √T Using the derivative rules learned in our course,…

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Q: 1. Evaluate the given integral Q. ² = £ Q L² L² (²x - 3) (x - y) dx dy

A: Let I=∫01∫y2yx-ydxdyI=∫01I2dyHere we…

Q: Show that x+iy | g+ix / = 1₁ =1, where X +iy and y+ix are complex numbers.

A: Here, let evaluate x+iyy+ix Using the absolute rule ab=|a||b|: =|x+iy||y+ix|

Q: zu 00{ " + uc}

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Q: 2. Using Linear Approximation, evaluate √81.4305 using the given function and initial valu below.…

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Q: Find the gradient of f(x,y,z) = (x² + y² + z²) Vf|(−2,2,− 1) = ₁ + Oj + k (Type integers or…

A: We want to find the gradient of the given function at point (-2,2,-1).

Q: M8 1 Σ n=1 h n’ + 8 +8 3

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Q: 3 Let f(x)=x* — x³. Determine the intervals where the function is - increasing/decreasing and…

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Q: 11. Find the limit using algebraic techniques. The limit of f(x) = -4 O- 0 O=¹ x+4 2x²+5x-12 as x…

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Q: Siven a = (1, 2, 1) and b - (k. 1, 2) and a × b = √35. X Determine the value(s) of k.

A: Follow the procedure given below.

Q: Evaluate the following integrals: (show solution) a x² +2 b.) 1 x+1 x+√x c) f(sec x d.) e 4x 4x+1 x…

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Q: 2 2 dx 2x (V2x + 9)

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Q: . Find the equation of the curve whose slope is the inverse of the sum of the square root of five…

A: Topic:- function  and application of integration

Q: [x³√₁-x² 2

A: ∫x31-x2dx=∫1-x2x3dx Let 1-x2=t⇒-2xdx=dt⇒xdx=-dt2                         =-∫(1-t)tdt2=-12∫(1-t)tdt…

Q: Evaluate the following limits. a. lim 2x 3x² b. lim x→0+ e-3/x ,2 X² ||

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Q: dy Assuming - 2x³ + 8y² + 6xy = 0 defines y as a differentiable function of x, use the theorem dx dy…

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Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: 5. Determine whether the following statements are True or False? y = f(x) 2 X 0 (a) lim f(x) = 1 (b)…

A: Given graph of y= f(x)

Q: (20-0) Given that = 5and 이히 = 3 1 6. Round your answer to one decimal place. = 3 and that (2a ›(à +…

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Q: 5. y" + 8y + 16y = 0

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Q: Consider the initial-value problem y' = 8x³y, y (2) = 5 Solve the initial-value problem to find the…

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Q: This question is designed to be answered with a calculator. A kettle of hot water, initially at…

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Q: 4) Given the points A(1, 2, 3), B(5, 4, 3), and C(2, 1, 2), find angle C

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Q: Suppose the functions f(x) and g(x) satisfy the following: f(2)= g(2) = g(0) = 4 3 2 = ƒ'(2) = g'(2)…

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Q: Find the area bounded by the line y = x+2 and parabola y = x².

A: We can solve this as follows: