Example:- Find the general solution of 1) xdy – ydx = 0 2) xcosh(y)dy – sinh (y) dx = 0 3)2dx – ev-*dy = 0 %3D

Q: Find (3+2)-2i. 406 754 386

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Q: Determine whether the following equation is separable. If so, solve the given initial value problem.…

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Q: Find the gradient vector field Vf of f. f(x, y, z) = xSye'/z Vf(x, у, 2) %3D

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Q: V3x - 2 lim tan- %3D x + V3

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Q: Evaluate the following limit using Taylor series. 7 7 tan -(x) – 7x + lim 4x° 7 7 tan "(х) - 7x +-…

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Q: Use the figure to evaluate the following function, given that f(x) = sin x. (Simplify your answer.…

A: Given diagram,

Q: Determine the radius and interval of convergence of the following power series. The radius of…

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Q: Q2/A) Find the particular solution for the following D.E., the boundary condition is (y-0@x

A: The given equation is dy=ex-ydx.

Q: Use implicit differentiation to find the gradient of the tangent line for xy 6xy - 2x = 9 at the…

A: topic- application of derivative

Q: from e'dv Ve4v -16

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Q: petdo eidj to noitom paidi b noit t no eog edt bnt Use the limit process to find the area of the…

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Q: Find r'(t). r(t) = (tan-(7t))i+t cos(t)j – Vēk

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Q: 3) Find an equation for the tangent line to the graph at the specified value of x. y=x²V5-x² ,x=1

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Q: (-2,0,5) and (–1,2, 3). Find an equation of the sphere whose endpoints of a diameter are

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Q: Consider the lines l : = 2 – y = z +1 and l2 : y - 2 3 1. Determine a direction vectors for the…

A: Consider the lines L1: x-12=2-y=z+1 and L2: 1-x2=y-2=z-33.1 To determine a direction vectors for the…

Q: y = 4x (4. 4) y 2x-4 5 (1,-2) Using a horizontal element of area, the area of the shaded region is…

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Q: 5. f(x) = (3x² + x)e5x² %3D

A: Explanation of the answer is as follows

Q: Find the differential dy and evaluate dy for the given values of x and d.x y = Vx2 + 24, x = 1, dx =…

A: First differentiate with respect to x then find value at x=1 and dx=-0.1

Q: r0.5 .2 X- dx (lerror| < 0.001)

A: Given I = ∫00.5 x3 e-x2 dx =− ( x2 + 1 ) e-x220.50

Q: Find the constant a, such that the function is continuous on the entire real line. ( 2x², f(x) = if…

A: Given the function is f(x) = 2x2,if  x≥1ax-1,if  x&lt;1

Q: 0 in quadrant II, find the exact value of: 81 If sin 0= sin 0+ sin 0+ 6. (Type an exact answer using…

A: topic - trigonometric identities sin(a+b)=sin(a)cos(b)-cos(a)sin(b)

Q: dx 9- x 15.

A: Topic = Integration As per guidelines , At  a time only one question can be answered out of…

Q: If f(x) = 8+r dt, find f(1).

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Q: 3n° + 2n³ - 7 {a,}== 7n' + 3п +4

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Q: Determine the area of the gtven reglon. y = x + sin X Step 1 Note that for the glven reglon, x…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: show

A: As per the guidelines we can solve 3 parts only.

Q: Evaluate the following limit using Taylor series. 7 7 tan 1(x) – 7x+: lim 4x° 7 .3 7 tan (x) – 7x +…

A: Given problem:-

Q: Find an explicit formula for an. 1 1 4'9' 1 1 14) 1, 16' 25

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Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

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Q: The junior class has 50 students. Fifteen students take only French, 5 students take only Latin, and…

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Q: Evaluate the definite integral. O e10 e10 - 1 i+ k 10 10 - 1) j+ k 1- e10 - 1 10 e10 i - e j+ 1 k 2…

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Q: If f is just that = e*[- sin(x + y) + cos(x +y)] and -e sin(x+y) which if the %3D ay following is…

A: On solving this we will get:- Option (A) is correct.

Q: =

A: We will find the derivative.

Q: y x/x, x-4, and y =0 -2

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Q: Find the area inside the oval limaçon r=7+3 sin 0. The area inside the oval limaçon is (Tuno uor…

A: we have to find the area.

Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the…

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

Q: Calculate the following derivative if f(x) = 5e* - x³. %3D (Use symbolic notation and fractions…

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Q: Problem 11. Solve the following system and express your solutions (if any) as individual ordered…

A: 3x2-2y2=-5     2x2+4y2=18

Q: A particle moves with its position given by z = cos(t) and y = sin(), where positions are given in…

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Q: Using the definition of the derivative, find f'(x) for the following function. 3. f(x) = x² – 3x + 8…

A: Here We have to use the definition of the derivative.

Q: sin ® 3y cos3ydy cos 3y dy

A: We have to find out the integral

Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) (1 + x)3 Σ 00 f(x) n =…

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Q: Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is…

A: Ratio Test : Suppose we have a series  ∑ an.Define,   L =limn→∞ an+1an .The,(i)  If L&lt;1 then…

Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: 3. (D² + 1)y = sec² x tan x. %3D

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Q: Area Between Two Regions Name: (a,h) (0, 0) (b,0) Use integration to determine the area of the…

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Q: sec 1.)S Intanßtanß dß

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Q: Find div F and curl F if F(x, y, z) = xz°i + 2y°r*j+ 6z*yk. div F=2° + 16 y' x+ 12 zy curl F=

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Q: 3. If f(x) = [ 8+f dt ,find f'(1). .

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Q: ind 4 using implicit differentiation and evaluate the derivative at point (-1,2) 2.a°y + 5x?y³ = 2x

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