Examples: Find the limits of the following: 4. lim tanx tan"(-0) = - 2 5. lim secx = lim cos (-) = cos 0 = 2 %3D 6. lim secx = x= lim cos (-) = cos"0 = " 7. lim cscx = lim sin(-) = sin 0 =0 8. lim csc x lim sin ) = sin0 = 0 %3D

Q: (Inºx– 3lnx) +dx (A Inx B Inºx © Intx D In x- 3lnx E In x- 3 (F) None

A: The integral is  ∫ln6x-3lnx4xdx

Q: Read each of the two statements carefully. Choose A(if both statements are true), B(if the 1st state...

A: Given that, There are two statement following, 1st : xsiny' = (x2 + 1)(y''')4 is a 4th degree ODE. 2...

Q: The graph of a function f is shown. Does f satisfy the hypotheses of the Mean Value Theorem on the i...

A: topic - mean value theorem

Q: WHich of the following represents the shell height if the shell method will be used to find the volu...

A: For Understanding of the shell method (Revolution about the x-axis):

Q: dx 5+ x2 хах 5+ x2 5+ x2

A:

Q: Jack buys calculators for $6.00 each, envelopes for $.50 each and pens for $1.50 each. He spends a t...

A: Jack buys calculators for $6.00 each, envelopes for $.50 each and pens for $1.50 each. He spends a t...

Q: Express the following sum in closed form. 6 +4. n k=1 k Hint: Start by multiplying out 6+4. n Note: ...

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Q: Given vector function: 7 (t) = (sin t, cos t, t) Find the following: (show complete solution). a. Fi...

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Q: Solve for the orthogonal trajectories x²(3k – x) – ky² = xy?

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Q: Use any method to determine whether the series converge. 1. (a) 19k k=1 The series 00 1 (b) 19 + 1 k...

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Q: Vミ-2 lim ミー→4 -4

A: Let, L=limz→ 4z-2z-4Rationalize Numerator L=limz→ 4z-2z-4z+2z+2 L=limz→ 4z-4(z-4)(z+2)L=limz→ 41(z+2...

Q: A gutter with trapezoidal cross section is to be made from a long sheet of tin that is 15 inches wid...

A: Trapezoidal  and geometrical area 

Q: c) Solve the following differential equations using the "exponential shift" defined by equation 4.1....

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Q: dz Find in the function ryz + a’yz = cos (xyz) CoS az

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Q: solve the differential eq + 2x) dx = = (2y \1+x²y² |dy 1+x²y²

A: The given differential equation is: y1+x2y2+2xdx=2y-x1+x2y2dy

Q: Model the height h of a projectile as a function of the time t it is in the air, with h(0) as the in...

A: Domain in this context mean that the values of t which makes height greater than or equal to zero. S...

Q: y = 5t2 - 2t + 4 -'(t) =

A: Given query is to find the derivative of the expression.

Q: A. FUNCT 1. Solve for the Range and Domain of the given function: g(t) = v4 – 7t %3D

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Q: 3x2 sin? x dx

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Q: x 2 Graph of f The function fis continuous for -4 <x54. The graph off shown above consists of five l...

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Q: IV. sec (3x) tan(3x) 12. Value of "F(b)" D. 1 A.0 Value of "F(a)" A.0 B.-2/3 C-2/3 13. B.-2/3 C-2/3 ...

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Q: Write the first five terms of the sequence, give the exact answer: n n + 23 n=1 Determine whether th...

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Q: ソニqett 10 =50e-0,0357+ 5oe ○.2 ニe-0,0357ナ Inco.2)ニ =-0.3577 Tニ

A: y=aekt10=50e-0.0357tDivide 50 on both side1050=e-0.0357t15=e-0.0357t0.2=e-0.0357tapply ln on both si...

Q: In the integral, cos?tsin2tdt , the correct u using general power formula is;

A: Here,              We have given a definite integration               now we have to solve this by u...

Q: Elimination of Arbitrary Constant: bxy +b*x+1=0;b is constant

A: We can find the answer as below.

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: 3. y = V(4x + 3)³

A: To find the third derivative of  y=(4x+3)34⇒y=(4x+3)34

Q: Use the definition of the derivative (long method/ increment method) to find the derivative of the f...

A: We will find the derivatives. 

Q: Write down a formula for ∂z/∂y if z is defined implicitly as a function of x and y by the equation b...

A: The given equation is yz=e3x+z.

Q: To evaluate the integral expression / sin -1(Vx ) dv, using simple substitution dv =f (x)dx_ Determi...

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Q: How to solve the integral of (x+2)/(x+4)? Apparently division with rational functions is required

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Q: Find the general term of the sequence, starting with n = 1, determine whether the sequence converges...

A: Let's find. 

Q: 19. e* +e = e**y

A: Solution ) ex + ey = ex + y  Differentiate with respect to x d/dx ( ex + ey )  = d/dx ( ex + y ) [ f...

Q: Vrite the first five terms of the sequence: +o0 ´13 In n n n=1 Determine whether the sequence conver...

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Q: I Eliminate the arbitrary constants y = C,e -2x COs 2x + ce <-2% SIn 3X

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Q: Which of the following integral will give the volume of a solid generated when the area bounded by y...

A: We have to find volume generated when area is rotated about x-axis.

Q: Which of the following integrals will yield an inverse trigonometric function? e2x dx 4+e2x wdw (B 2...

A: Let I=∫19-16x2dxI=∫11-16x29dxI=∫112-43x2dxWe know tha ∫1a2-x2dx=sin-1xa+CThereoreI=sin-143x1+CI=sin-...

Q: Given the function: z = e*+y sin (x + y) dz a. Compute the ду b. Compute the dz show complete soluti...

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Q: The DE for the family of circles of radius 9 is: A [1+ (y')²]³+81=0 B ® [1+(y")*]³–81=o [1+(y')²]³– ...

A: The general equation of the circle with center (h,k) and radius r is             ( x - h )2 + ( y - ...

Q: Find for the following function. dx 4 sin x y = 9 -8 sin x dy dx II

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Q: Use integration by parts to evaluate the definite integral te dt. CHECK ANSWER

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Q: 9-30. Shell method Let R be the region bounded by the following curves. Use the shell method to find...

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Q: Q3/ find the derivative La)= メ 2. logs (x+3) 2x+4

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Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as improper f...

A: Here we have to find out the convergence of The infinite series and then we find out the sum if it c...

Q: In2| 4+ tan-'cos- dx 2 sin ( 1+cos | 4+ tan-'cos- 2sin- · In²| 4+ tan-'cos- dx 2 (A 1+cos- 4+ tan-'c...

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Q: (x+2)2 dx (x+2)3 +C (A + 2x+4 In x +C +4x +4 In x + C (x+2)3 D -In x +C 3. B.

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Q: Assume that functions f and g are differentiable with f(- 3) = 4, f'(- 3) = - 4, g(- 3) = - 4, and g...

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Q: If f(x)dx=cot x² +C , then f (x) is equal to A -2cscx? B -2xcsc?x? © In/cscx²| D O In/sinx²|

A: We have to choose correct option for value of f(x)

Q: Express the repeating decimal as a fraction. 0.2513 23 23 23...

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Q: The quantity of charge Q in coulombs (C) that has passed through a point in a wire up to time t (mea...

A: we have given Q 

Q: Set-up the integral to calculate the area of a region bounded by х-у-3 and y-x2 -6x+9? A dy dx x2— б...

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