dx x³Vx? – 16

Q: Determine the area of the given region. 3. Region between f(x) = x - 4x and g(x) = x.

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Q: 1. Find the second derivative of the parametric equations x = a cos t and y = b sin t 2. Use second…

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Q: 4. Solve 5x3 - 3x2 – 32x – 12 = 0

A: We have to solve the equation

Q: Evaluate: de (1-a)

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Q: g'(θ) at θ = π/3 if g(θ) = θsinθ

A: Given: g(θ) = θsinθ      , θ= π3

Q: (22) Find the derivative of f(2)

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Q: 3) lim X -3x2 + 8x – 2 6x2 + 5 A) - B) 0 D) =

A: This question can be solved using the concept of indeterminate form and L Hospital's Rule.

Q: Evaluate the limit using techniques from Chapters 2 and 4 and using L'Hoptal's Rule. 3(x-7) Iim x…

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Q: Use Partial Fractions x* + 3x? – x – 8 dx x3 + 4x

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Q: the product z1 z2 in polar form? Z1 = 3 cis z2 = 4 cis - cis (금) cis () 7x 2 cis ()

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Q: 06. lim, ,xCsC x xcsC X

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Q: Evaluate: sin 6x sin 3a da A. 0 в. - В. 2 C. - :- С. 2 D.

A: SOLUTION-

Q: 1-x -x? dy dx -1 J-V1-x² (1 + x + y)² X.

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Q: (27) Evaluate the integral: 1 IP: 5t + 4)2.7 dt

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Q: 1+ VT (20) Evaluate the integral: -dx. (01) I 1:6

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Q: Find the directional derivative of the function f(z, y) = In(z° + y*) at the point (3, – 1) in the…

A: We can solve this as follows:

Q: Find all solutions of the equation in the interval 0, 2n). 3 sin 0+1= 1 Write your answer in radians…

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Q: Inx 1 13. lim, X X,

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Q: Determine whether the SEQUENCE converges or diverges. If it converges, find the limit: 3x n+4n-V5…

A: If the limit of the sequences is finite then it is convergent.

Q: Find a vector that is perpendicular to the given vectors. 3) i = (-5, 6, 7) v = 1, -9, 0) 4) RS and…

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Q: 0 1 7) [ [ysin x dxdy -1 -y

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Q: The value of the triple integral /I| 2x dV where E is the region E inside both x2 + y + z? = 36 and…

A: See the solution in below

Q: 8 Given a function: f(x) (х-7)(х-1) Write down the definition that lim f (x) = L X→a = -1| 8 Prove…

A: We have to prove the given condition

Q: Evaluate the limit using techniques from Chapters 2 and 4 and using L'Hopital's Rule. sin(9x) lim 7x…

A: We have to find the limit

Q: 9. A rectangle is formed in R² by the vectors OA = (1, 3) and OB = (6, –1). a) Calculate the…

A: a)Given OA=i+3jOB=6i-jSince OC is diagonal of parallelgram ABCDOC=OA+OBOC=i+3j+6i-jOC=7i+2j

Q: (24) Evaluate the integral: / Va sin(1+ x/²)dx. (25) Find the equation of the normal line to the…

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Q: Evaluate the integral: 1. Jcsc x (сos? х — 1)dx 2. S(sec2 x + csc² x) cos? x dx 3. S(wew² + w²ew³)…

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Q: 1 (27) Evaluate the integral: (5t + 4)2.7

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Q: An earthquake was recorded with an intensity which was 630,957 times more powerful than a reference…

A: Given that I=630957×I0

Q: Convert to a rectangular coon 12. (3,*)

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Q: 8 Given a function: f(x) = (х-7)(х-1) Write down the definition that lim f (x) = L -1| х-5 (х-7)…

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Q: What is the exact value of csc(– 1305°)? V3 A B D 2.

A: using csc(-x)=-csc(x) and  csc(360n+x)=csc(x)

Q: noitel arctan 2x 37. lim x→0+ In x

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Q: 1. Describe the transformations of the graph of y=vx to obtain the graphs of the following…

A: Question- 1. Describe the transformations of the graph of y=√x to obtain the graphs of the following…

Q: 11. y = x + x

A: Given

Q: cos(0)tan(8) sec? (ө) — 1 is written in terms of sin(e) only and simplified, what is the resulting…

A: Topic:- trigonometry

Q: What is the derivative of sin(2x) at the point (0,0)? O 2 O -2 O 4

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Q: rV1-y² (x² + y³) dy dx -1 J-V1-y

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Q: Complete the proof of the identity by choosing the Rule that justifies each step. sin'x+ 3 cos?x=1+2…

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Q: Find the first term and the common difference for the arithmetic sequence. Round approximations to…

A: Use formula of arithmetic progression

Q: The graph of y= sin(x) shifts T units to the left and units upward. Which of the following functions…

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Q: Graph the function. 6x + 4, if x< 0 f(x) = 5x2 - 3, if x20 OA. OB. Oc. OD.

A: given function is f(x)=6x+4, if x&lt;05x2-3,if x≥0 so we calculate the values of f(x) for few values…

Q: Supply the missing integrand and the limits of integration -2 x dx dy _dy V4 + x2 I V4+x=dy В -2)dy…

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Q: The graph of a function f is given. Use the graph to find the value f1 (3). Q 6-

A: For inverse function value of x and y get interchanged   Given f-1(x)=f-1(3) x = 3 , y = ? as  value…

Q: Use the specified substitution to find or evaluate the Integral. 3. dx Vx(1 + x) = Vx

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Q: 1+sin (n) 2. Determine whether the series is convergent explain why. Ln=1

A: We have to test the series

Q: Find dy/dx by Implicit differentlation. x = 7 In(y- 24), (0, 5) Ap dx Find the slope of the graph at…

A: implicit derivative dydx of equation x=7lny2-24

Q: y+4 =-V2x

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Q: (24) Evaluate the integral: | Væ sin(1+ r/²)dx.

A: Solution:   As per our guidelines we are supposed to answer only? One question ( if there are…

Q: Find the area of the following shape, 212 2/2 9/2

A: We have to find the area of the given shape