x2+64 Using trigonometric substitution, given dx, the simplified form of the integral is: x2 sec Odo tan2e True False

Q: Q3) Evaluate triple integral (x2 - y?)dz dx dy.

A:

Q: 8:44 C ing e Determine whether the series is convergent or divergent. 00 1 n = 1 The series is a…

A:

Q: DO NOT include spaces in between characters. * Using implicit differentiation, find the slope of the…

A: We can solve this as follows:

Q: A man 6 ft tall is walking at the rate of 3 ft/sec toward a streetlight 20 ft high. At what rate (in…

A:

Q: Remember, even if you enter an answer rounded to a set number of decimal places, if you use that…

A: Law of sines : sin Aa = sin Bb = sin Cc Given  ∠A=38.8°,  a=182.4,  b=248.6

Q: Find the volume of the solid that results when the shaded region is Y = x revolved about the…

A:

Q: Use the Trapezoidal rule with step size Ar = 1 to appoximate the integral f(x)dx where a table of…

A:

Q: Q2) Convert the polar function r tan20 to cartesian.

A:

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

A:

Q: 3 5 8x 15 dx 5 x4 |

A:

Q: 2.Find the indicated limit or state that is does not exist x* – y* C. lim (x,y)→(0,0) x² +y ху d.…

A: Solving

Q: Su Find D. andR %3D

A: Domain is the set of input values for which the function is defined. Range is the set of output…

Q: d) (i) Use the alternating series test to show that the series converges. k+1 k +3 Σ-) k(k+1) k=1

A: To show that the given series converges using alternating test.

Q: Q1: Find the integration of : (choose 3 only ) 1. Sc (3 sin x)cos (4 sin x). cosxdx Cos

A:

Q: A particle is moving in space and its position at time t is given by r(t) 4(cos t)i+ 4(sin t)j+ /²k,…

A: Given problem:-

Q: Q2) Convert the polar function r tan20 to cartesian.

A:

Q: nsider Evaluate дхду

A: Given,             z=ex3+y2To find : Evaluate ∂2z∂x∂y

Q: Q2) Solve the D.E xy(x? + 1)dy - (y? + 1)dx = 0 %3D

A:

Q: Consider --e +y?). 3+3² Evaluate dxdy

A: We have to find partial derivatives for the given function.

Q: Question 6 The tangent to the curve y = 1/x intersects the r-axis at (v2,0). What is its…

A: The tangent to the curve y=1x, intersects the x‐axis at 2, 0.To determine its y‐intercept.

Q: Using implicit differentiation, find the slope of the tangent line at the point (9,16) on the curve…

A:

Q: Qel Find the limis hth G8h alie んう0 2lim 土 2x2_8

A:

Q: Evaluate s 2°ds Oa 2 (sln2-1) (In2)2 2" In2 Oc sin2-1) (In2)2

A:

Q: Q4) Find plane area inside the polar function r = 2sin E- 0) and outside r= sin -0) in first…

A:

Q: |x= 8| f (x) = Evaluate the left-hand limit of as X8. 16- 2x O 1/2

A: Given,            fx=x-816-2x as x→8To find : Evaluate the left-hand limit of the given function.

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

A:

Q: + C2e¬4x The auxiliary equation of a second-order homogeneous linear differential equation is m2 –…

A:

Q: Q3) Evaluate triple integral dz dy dx.

A: A detailed solution is given below

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 Ju. (v x w)| to determine…

A:

Q: Choose the suitable function y1, for the method of reduction of order, to find a second solution y2…

A:

Q: Which of the following yields the value 3187 (8r+7y)dudy (8r+7y)dydx (8r+7)dudy O none of the oices

A:

Q: Q4) Evaluate the following integral using Trigonometric Substitutions Method: 2 y = - x dx

A:

Q: Example Evaluate +f -P) dpdgdr (p2 + q² – r²) dp dq dr + pq² – pr2 dq dr 3 1 + q? ² – r? } dqdr 3 -…

A: Let's find.

Q: For item # 6, use the product rule. 6.) f (x) = (x³ – 1)(4x + 5) %3D | x+3 7.) f (x) = 5х-2

A: Here we have to differentiate the given functions.

Q: (e) Suppose that the functionf is represented by the power series f (x) =1- +(-1)*. - -- +... 2 4 8.…

A:

Q: Reduction of order can be used with 2x to find a second solution for the %D DE: 2x²y" – xy' - 2y =…

A: Given y1= 2x² is a solution of 2x²y''-xy'-2y=0....(i) So 2x²y1''-xy1'-2y1=0....(ii) Let y=…

Q: Q5) Find volume of body bounded by z = 0 from below and z = 4- y from above inside y = x2 ,y = 4.

A: Set up the triple integral and solve to get the desired volume.

Q: 6.Find all the first partial derivatives of each function x² – y² c. f(x,y) ху с. = d. f(x,y)=e* cos…

A:

Q: Q3 Find y ン ニ月(^)→ t(メッ) tanx 2 y-(1+x)

A:

Q: Q3) Find the Area bounded by the curves y? = x and x = 2y – y?.

A: The given curves are; y2=x & x=2y-y2   Now find the point of intersection between the curve y2=x…

Q: csc 2 5x cot 5x dx, can be evaluated conveniently using Trigonometric Transformation. ( A) True…

A:

Q: Q14. The value of lim et3 -x tan x-cos x x2 is? -

A: use l hospital rule for solving for the integral.

Q: Q3/ Solve the following equation by (Finite Difference Method), choose (h= 0.5) *+ 2y = 3 ,y (0) =…

A:

Q: Find the slope of the tangent line of the function y = In (x) at x = e2 O1/e? 4/et O 1/e* O 2le2

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

Q: Q4) Find plane area inside the polar function r = 2sin E-0) and outside T= sin in-e) in first…

A:

Q: to this answer. Evaluate the left-hand limit of as f (x) = x8. 16-2x O 1/2 O -1/2 O undefined

A:

Q: Find the value of x such that x satisfies the mean-value theorem at the interval [0. 1] for the…

A:

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: Give the VALUE only. No need to inclu unit. *

A: Given: s=24t+10t2