Evaluate f Vr+ V?dx Oa. 3 am +2) +C (V2) +C can) Ob. 2 am +2) +C 30 om +C (25) Oc 2 an +m) +C O d. 5

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

A: We know that x = rcosθ, y=rsinθ Given: r=tan2θ

Q: Let y=f(x).Which of the following correctly defines dx [fk+Ax)-fw] a. lim Ax+xL Ax Ob. lim Ax+x…

A:

Q: Question For the function given below, which statements concerning Rolle's theorem are true? —3х - 1…

A: This question is related to Rolle's theorem, we will solve it using given information.

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

A: We will use simple Integration rules to solve this question.

Q: 1 Calculate the difference quotient for f(x) = at a = 4. V2x + 7 (Express numbers in exact form. Use…

A:

Q: Find the olar eauatiDo for the Curve represented by the given Cartesian eawation.

A:

Q: Evaluate the limit, if it exists: x²-9 lim *-3 X+ 3 does not exist -6 1

A:

Q: Given that x=t3+t and y=3/2t4+t2, find dy/dx, d2y/dx2, d3y/dx3

A:

Q: (x-2)" En=0 n2+1 n3D0

A:

Q: Determine the general equation of the plane Ω passing through the point P(−5,−4,1) and parallel to…

A:

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: 1. Solve letter a and letter b. Show t complete solution. а. Find of the dy dx function 9x* + tany…

A: Topic:- derivatives

Q: 2. Sketch the plane curve by plotting points then indicate the orientation of the curve. x = t2 – 4…

A:

Q: Identify if the following series is convergent or divergent: 00 (-1)"3n² 4n2–1 n=1

A:

Q: Evaluate the following iterated integral. 2 16 15y dx dy 2.

A:

Q: Is this series convergent or divergent?

A: This question can be solved using the concept of root test.

Q: f(x) – f(2) x - 2 Find the difference quotient when f(x) = 2 + 4x + 5x². Simplify the expression…

A:

Q: 8. (5x'-4x +8x) dx

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

Q: Q2: Find the integration by applying substitution method: 7 dX (X – 1)VX2 – 2x - 48

A: Given,             ∫7x-1x2-2x-48dx

Q: Q3) Find the Area bounded by the curves x and x = 2y – y².

A: Topic = Area Area bounded by curves is 13.

Q: Determine the equation of the tangent to the graph of y = [2~/x - x][1+ /x - x ] at the point (1,…

A:

Q: For the functionf(x) given below, evaluate lim f(x) and lim f(x). x00 X→ー0 f(x) = -5x - 3x + 2 cos…

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: Consider the parallelepiped with adjacent edges u = 9i + 5j + k v = i+j+ 8k w = i+ 2j + 8k Find the…

A:

Q: find the derivative and simplify the answer sin² (esin t) + cos-{(2t3 – 5)

A:

Q: Evaluate the following double integral over the region R. 7 x-y') dA; R= {(x,y): 0<xS1, -1sys1}…

A: Here we have to evaluate the given double integral over the region R .

Q: Determine if the given series is convergent or divergent. 3" en – 2" n=1 2.

A:

Q: Use Newton's Method to approximate the zero(s) of the function. Continue the iterations until two…

A:

Q: x2 – 125 lim x→-5+ x2 + 4x – 5

A:

Q: n(A U B) = 55, n(AN B) = 15, and n(B) = 35 %3D Find the value of x A 15 y

A:

Q: Express the shaded area of the region shown below by double integrals of order of integration (1)…

A:

Q: Σ (-1)" n=1 3-4n-1

A: topic - geometric series

Q: メ +) メ +2 3. 2. メナ 3 メナ」 メト2 メ + 3

A: To find for what values of x determinant is 0.

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: Solve the D.E dy – (2x/1- y2)dx = 0

A:

Q: Let r(t) = (t2, 1 - t, 4t). Calculate the derivative of r(t) a(t) at t = 4, assuming that a(4) = (9,…

A:

Q: Find the saddle pointis of the function f(x,y) = x° +y°+i y+4 Oa(5-1) Oc (4.0) & (4,0) Od(0.0)

A:

Q: Show that the lines L1 : x = 5 – t, y = 2t, z = 1+t and L2 : x = 1+ 2t, y = 3 – 4t, z = 5 – 2t are…

A:

Q: Find f"(1) if Ax) = X+1. %3D 1 1 1/4 12 OOO

A: To find f'1 if fx=xx+1.

Q: 4 4-y Q3) Evaluate triple integral , S S dz dy dx

A: I have stated the used formulas in the solution

Q: Evaluate the following integral using Partial Fractions Method: x³ + x? y = dx х2 + х — 2 -

A: Follow the procedure given below.

Q: The height of a ball t seconds after it is thrown upward from a height of 5 feet and with an initial…

A:

Q: 1. Find the indicated limit or state that is does not exist lim (3x'y- xy³) а. (x,y)→(1,3) b.…

A:

Q: is satisfied. Finally, to determine if Rolle's Theorem can be applied, we also need to check if the…

A:

Q: tan²x dx, can be evaluated by using trigonometric transformation . A True False

A: The given integral is: I=∫sec5xtan2xdx Use the derivarive: ddx(secx)=tan2x

Q: 1 Evaluate: xInx In Oc -In 6 O d. In 6 l3.

A: The given problem is solved below in detail.

Q: Evaluate the following integral using Partial Fractions Method: x3 + x2 y = dx x² + x – 2

A: Let…

Q: xist enter DNE.

A:

Q: Determine if the following functions are continuous at the given value of x. 1. f(x) = 3x? + 2x + 1…

A: continuty

Q: х2 — бх + 9 dx V6x – x2

A: