Vx+1 -1 14. lim A. DNE В. О C. 00 D. -00

Q: 2x² sin x + 3y³ 3x³ + 2y² lim (x,y)→(0,0) if we approach along y-axis, we will get Select one: True…

A: This question is based on two variable limits.

Q: y = Arctan(sec (3x)) +ncot(2x)

A: Given: y = tan-1sec3x + πcot2x To find: The value of dydx

Q: 38. A. -arcsin x x Vx2 – a² 39. 1 В. -arccos x a2 + x2 40. 1 С. | -arccot x Va? – x2 - D. -arccs x…

A: Match the following

Q: COS X lim X0 ex

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Q: 1 2. y = arctan 2 2(x2 + 4) -1 3.. y = 4 coth(9x – 3) |

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Q: Find the 2x -3 lim 4x +1 DNE O 1/2 2. What is the

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Q: Determine whether the following statements is true or false, and explain why.

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Q: Show that

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Q: 3e2* -1 d) lim 2x 4e* +cos x

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Q: 3x;" + (х)? Дх, [3, 4] lim i = 1 '4 dx

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Q: b) Z = Arctan ( x² /y³)

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Q: 1. D'y+y=sec x² 2. D'y+y= tanx

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Q: y" "yi g= coshox + sinhɔxi

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Q: 46-% dy dx change bheorder and eva/ute.

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Q: (c) 1 lim – cos(6r) 5x

A: Explanation of the solution is given below...

Q: If y = tanh"(k/x) and x (1 - 144x) y'=A Then A= .

A: First we find the derivative of the given function y.  After that we substitute k=12 in the result…

Q: 15. y=Arccos (x²)

A: The given function is: y=Arccosx2   As we know that: The Chain Rule: fgx'=f'gx·g'x The Power Law:…

Q: y=2(21,2-1 + arctan x) 2 2 x-1

A: Please see the whiteboard.

Q: i tan?(x) sec(x) dx trig property 2.

A: We have to find the integration

Q: ex+e¬x_x²-2 3. lim X--0 SIN²X-x2

A: The given limit  limx→0ex+e-x-x2-2sin2x-x2 This limit is in 0/0 form, so we can apply L' Hospital's…

Q: y = 8x arccos(x - 1) y =

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Q: dy 2 3 ...2 C05X +sinx...y.-(4x+5). y. ---

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Q: 1 у? sin y 2)lim y→∞ y + /2y3 –1

A: We can find the limit as below.

Q: fxcos (x)dx COS

A: Assume u=x^2Find du

Q: Find the derivative of the function

A: Given: y=1212lnx+1x-1+tan-1x for finding derivative of given expression, first we simplify it…

Q: 2) Sketch: y = -x(x + 50)(x – 1000)(x + 1)

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Q: y=3x^(3/2) on [2,4] find arclength

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Q: d) lim cos x sec (5x)

A: The given expression is :  limx→π-2cosx sex5x  Let,  x+h=π2  As x→π-2 so, h→0  cosx sec5x=cosπ2-h…

Q: 2+X y = Arccot x+ Arctan 1-2x

A: To determine the derivative of the the function ; y=Arccot x+Arctan2+x1-2x Differentiate both sides…

Q: 10. lim (x? sin () cscx) A. 0 В. 1/2 С. 2 D. DNE

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Q: 1. y = Arccos 1-x

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Q: d. 0.33 +3t-10 40. lim a. DNE sin(t+5) b-7 C7

A: We have to find the limit                                limt→-5t2+3t-10sint+5

Q: a) an a) —arctan– Tee d) 1 S x² - 1 1 1 34 1 b) arctan3 - - In2+ 풍 c) arct 3 1 dx -In 3+ arctan3+-In…

A: Given integral ∫2∞1x4-1dx. The objective is to evaluate the integral.

Q: x²-a? 6.) y'of y = arccos² х-а + arccsc + arcsin- x²-a² a 7.) y"ofy = (x – a)V2ax – x² + a²arcsin…

A: Given  Y=arccosx2-a2x+arccscx-aa+ arcsinax2-a2

Q: 4) lim (ei – 1) x 3

A: Let's find.

Q: 2U y'sy tan(x) 2) yy's 2Xes

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Q: tan(xy) = ? lim (х, у) >(,0) у+ 2ху 1 (c) 3 (а) 0 (b) (d) (е) 1

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Q: dx lim dx %3D

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Q: i) Solve: (1+ yNdx = (tan-y- x)dy. %3D

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Q: y = Arctan 2+x 1-2x

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Q: -5t i + j+ sin(3t) k sin (t) lim e t 0

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Q: It x= Arctant3, y=/1+76, find the value of a if 2ay" =17 when 1=/2- y' O 2/2 O -22

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Q: tan(xy) - 2 lim (х, у) ->(1,0) у + 2хy (a) 0 (b) (c) (d) (e) 1

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Q: ■ Find the limit.

A: The expression given is, limx→∞x2+ax-x2+bx. To find the limit of the function ,  Multiply and divide…

Q: 9 y- Arctan( 1-2x

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Q: (cos(3x+ 1))² lim 7+ 4x

A: our objective is to find the limit