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Q: Use the limit definition to compute the derivative of the function f(x) = Vx + 2 at x = 1. (Use…

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Q: X+ 1 Evaluate lim x→1* ** - 5x +4• | O-1 OO OO

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Q: Use the appropriate Product Rule to evaluate the derivative, where ri(t) = (9t, -10, -t°),r2(t) =…

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Q: dy = Solve 2xy r x2 + y? given that y = 0 at a = 1 %3D

A: To find particular solution of D.E.

Q: Obtain the general solution unless otherwise instructed A. LINEAR EQUATIONS WITH CONSTANT…

A: Note:- These are multiple questions and according to our company guideline we can do maximum one…

Q: Consider the parametric curve defined by x=3+5t and y=1+3t Over which values of , does the curve has…

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Q: Describe the largest set S on which it is correct to say that f is continuous хx* + ху — 5 а. f(х,…

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Q: Solve the D.E dy – (2x/1- y2)dx = 0

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Q: Question 3 2 dr sech 2r = A True B) False

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Q: Water is pouring into a swimming pool. After t hours, there are t + sqrt(t) gallons in the pool. At…

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Q: Consider Evaluate (ar +6r)e' (6r*+9x)e

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Q: 1-y -x. dy at the point (0,1) given the curve dx Find the value of 1+y

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Q: 1.5 3-y Q1) Evaluate the integral dx dy

A: To evaluate the given integral.

Q: 0.125 А. f(8t) dt | 0. 0.25 B. f(1 – 4t) dt = 2.5 c. f(5 – 2t) dt =

A: Given that,

Q: Consider the solid bounded by the planes: =x+y, z=30, x=0, y=0. Determine the volume of the solid.

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Q: 10 if f(x)= t +P, then %3D f'(X) = f'(-2)=

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Q: Show that the set of all points P that are twice as far from (-1,5,3) as from (6,2, –2) is a sphere.…

A: The set of all points P that are  twice as far from -1, 5, 3 as from 6, 2, -2. Let coordinate of a…

Q: 3. A body moves along a horizontal line in accordance to s= t3 + 9t2 + 24t. Find the total distance…

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Q: Apply the chain rule to differentiate the following functions. Show your complete solutions and…

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question. If…

Q: 36. (х, у) —- (0, 0) lim (x + y²) In(x² + y²)

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Q: Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx y =

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Q: 12x 3 3 15 12 x4

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Q: : / yº sech(e™mv) tanh (» ) dy 7lny Evaluate: @ -ch(7) + C None

A: Given problem:- ∫ y6 sech(e7ln(y)) tanh(e7ln(y)) dy

Q: 4. Find the Laurent series of the following function : f (z) = (z + 1)(z + 3) 1 region 2 < |z – 1| <…

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Q: applying substitution méthöd: sqns -48

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Q: Evaluate f s 2°ds О а. 2"(sin2 - 1) (In2)2 O b. 2(sln2 - 1) (In2)2 O C. 2* In2 O d. 25 In2

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Q: Consider ,- (x3+y²). Evaluate dx² O (9x4+6x)e «³+y?) O (6r²+ 3x)e (x³+y?) O (6x4+9x)e (x³+y?) O…

A: I have stated the used formulas in the solution

Q: Descibe the level curves of the surface f(x.y)=x-4y. O a Hyperbolas Ob.Parabolas Oc Crdes Od Elipes

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Q: wolloi or oisuleu 6. (-3x+15x") dx 12x 15 12 dx 7. + 3 x'

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Q: 1 lim X0-x23

A: Given,limx→ 0-1x23We know that,For x approaching 0 from the left, x&lt;0  ⇒   x23&lt;0The…

Q: Q5) Find volume of body bounded by z2 + y2 + x2 = 4.

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Q: Find the surface area of the cone z = x² + y2 that lies between the plane y = x and the cylinder y =…

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Q: Evaluate the following integral using Trigonometric Substitutions Method: dx y = 9x² + 16

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Q: Question 4 -e-*) dx Evaluate: A '+C 2 B cosh x +C sinh x +C D – sinh x +C E None (F -cosh x +C 2

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Q: Ql: Find the integration of : 1. S cos (3 sin x)cos (4 sin x). cosxdx

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Q: Consider the region bounded by the curve v= x2 - 1 and the x - axis over the interval [0,3]. Find…

A: The equation for the x-axis is y=0. Draw the given two curves.

Q: Evaluate the following integral using three different orders of integration. SSL:(x: – y') dV, where…

A: Here we have to evaluate the given integral.

Q: Find each of the following indefinite integrals.  c. Z (r+2)^2/r^3 dr

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Q: Compute f'(a) using f'(a) = lim f(a + h) – f(@) or f'(a) = lim Tx) – J(d) for f(x) = 15x³, a = 2. or…

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Q: 3. Find the area of the band cut from the paraboloid x² + y? – z = 0 by the planes z = 2 and z = 6.…

A: Let's find.

Q: Determine a and b so that the function f(x) is continuous for all values of x. jika x <- 2 sin x…

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Q: 9. (D² – 2D + 5)²y = 0 10. (D² – 2D – 3)y = 0 when x = 0, y = 0, y' = –4 %3D -

A: We will solve auxiliary equation then we will find the solution.

Q: Ob.2 amom +C Evaluate +Vrdx Oa.5 2 5 3 2 Oc 2 wn +C Od 3 +C 2/3

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Q: What is 2x4

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Q: A rectangular piece of cardboard has a size of 45 x 24 cm. This cardboard will be made into a box…

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Q: Vx – 8 = xy + 2

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Q: Write the expression as a single logarithm. 4 log 27x-1 - log 2 + log 25 4 log 27x-1 - log 2 + log…

A: We have to simplify logarithm

Q: 2BVC = (12x - 24)° and mZEVD = (2x + 15. What is m2CVE ? THAM V. A D. Find the missing pieces.

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Q: inside polar functionr = 2 and outside p in third auartor

A: We have to find the area according to the given information

Q: An object moves with acceleration function a(t) = 5 + 2t – 9t². Its initial velocity is v(0) = 6 m/s…

A: Find out the position after t seconds.