(3 − |x|)dr is equal to L (3 (a) f( (3 - x) dx (b) [(3+z)dz (c) [²₁ (3 - x) dx + [² (3 + x) dx (d) [" (3+x)de+ [" (3-1)dx

Q: Find all the points of g(x, y) = x³ − 3x + 3xy² where a relative extrema might occur. ○ (−1,0) and…

A: To find out the critical points.

Q: Compute Au, where A Au = = 1 (56) 4 and u= (9).

A: The simple matrix product..

Q: 36. Which one of the following is true for all z ER? (a) z sin(2) dx = (1-2) cos(x) + C (c) (b)…

A: Now that we know that the integral of x sin x is equal to −x cos x + sin x + C, we will derive this…

Q: If an object is moving along a horizontal line, such that it's velocity, v(t) = cos(3t), what is the…

A:

Q: Q2/ Examine the following surface for maximum, minimum, and saddle points 2 = x² + y² + xy + 4x - 4y…

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Q: Q3) Find the integration by using Partial fraction method Y x² + 2x + 1 (x² + 1)² dx

A:

Q: 3x + 5, 13+¹6, Find a value of x, if any, at which f(x) = If f(x) is continuous for all values of x,…

A: Given: Notice that 3x+5 is continuous for x<4 and 13+16/x is continuous for x>4. Now, we need…

Q: If we let u = cos t, then the integral [(sint). In (cost) dt can be expressed as - [In(u) du 0…

A: An integral is given. We have to write the substitution form of the integration in terms of the…

Q: find dt' t= Счи) 11/2 (24)

A: We know that ddxxn=nxn-1

Q: 5) An equation of the of the plane passing through the points P(0,2,1), Q(2,1,2), and R(3,3,1).

A:

Q: 15. Given: Th: x+y+z=0 Find: the value of 'm T₂: x+2y+2z-1=0 That a line that lies on the plane 773:…

A:

Q: 7. Determine the area bounded by y = x² - 6x + 10, x = 1, x = 5 and the x-axis.

A: Above question is solved.

Q: Find the derivative y = x tan^¹x − In √√1 + x²

A:

Q: A) e-2 Β) e2 Σε e=2n =? 71=0 C) CADEMI Ε)

A:

Q: You want to build a 1100 square foot rectangular infinity pool. Three of the sides will have regular…

A:

Q: x+2 lim x-2x²+4x+4

A:

Q: 14. State whether the following pairs of planes intersect. If the planes intersect, determine the…

A: The planes are,π1: x-y+z-2=0 and π2: 2x+y+z-4=0

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A:

Q: Find the value of an investment of $25,000 for 13 years at an annual interest rate of 3.15%…

A:

Q: b. |ā + (bx c)|

A:

Q: Next question 1 5 Find the absolute extrema if they exist, as well as all values of x where they…

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Q: Answer the given problems in two ways: (1) by using Chain Rule (2) by finding f(g(x)), taking the…

A:

Q: -7-6-5-4-3-2- 6 5 4 3 -2 -5. -6. H 1 2 3 4 5 6 7

A:

Q: Use the quotient rule to find the derivative of the function. 3t² - 1 g(t) 2t + 5 =

A:

Q: 10. Show that these two lines are coincident. [x, y, z]= [1, 5, -2]+s[1, 7, -3] [x, y, z]=[-3, -23,…

A:

Q: State

A:

Q: 2 Σ(-1)+1n? + 5 m2 + 4 n=1

A:

Q: 9. The value of q will make the roots of quadratic equation 9x²-4qx+4=0 be equal are A.0 B. q-3,-3…

A:

Q: kx 4+x² If k 1, evaluate k (a) 2 kx (b) 2 J₁ arctan (2x) + C arctan (2x) + C dx. (c) // ln(x² + 4) +…

A:

Q: Which of the following conditions is NOT required for lim f(x) to exist? x→a

A:

Q: Find an antiderivative F(x) with F'(x) = f(x) = 8+21x² + 10x4 Remember to include a "+ C" if…

A: This question is based on indefinite integral.

Q: df What is the total change of f(x) between x = 0 and x = 2, when dx 2.132 2.101 1.709 1.609 = 2…

A: Given query is to find the total chnage .

Q: Q3: Find the length of y=√x+2,1 ≤ x ≤ 7, Using ds = Y 04 1+²dy rotating

A:

Q: Which of the following functions has a horizontal asymptote at y = 2?

A:

Q: Compute A B, where A AB= 0 -2 2 -2 0 2 -4 7 8 -5 -1 2 and B = 8 -2 1 -5 -1 3

A: This question can be solved using the concept of multiplication of matrices.

Q: Solve the differential equation (24xy + 40y²) + (8x² + 40xy)y' = using the integrating factor µ(x,…

A:

Q: Find the integration by using Partial fraction method x² + 2x + 1 (x² + 1)² dx

A:

Q: Use Newton's method to approximate a root of the equation e0.22² = 6 - as follows. Let #₁ = 1 be the…

A: Given :e0.2x2=6-xx1=1

Q: Suppose c is a real number, which of the following limits ALWAYS exist?

A:

Q: For the function y = f(x) f(x) = 1x³ + 5: df a. Find at x = = 4. dx ƒ'(4) = = 48 b. Find a formula…

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Q: Find the derivative (df/dx) 1- f(x) = cscx - 4√x + 7y-² 2-f(x)=x² cotx-x-2 3-f(x) = (secx + tanx)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Q3/Evaluate: ff(x + y) dy dx for the region bounded by the x = 0, x = 2, y=x and y=x+2

A: Given

Q: Let r(x) = f(g(h(x))), where h(1) = 5, g(5) = 2, h'(1) = 9, g'(5) = -2, and f'(2) = 5. Find r'(1).

A:

Q: Determine whether the differential equation (7x+8) + (7y - 7)y' = 0 is exact. If it is exact, find…

A: To determine that the differential equation is exact or not.

Q: (b) In an oil refinery, a storage tank as shown in Figure 1 contains 2000 gal of gasoline that…

A:

Q: hand-tossed pizza base starts off as a ball of dough with a volume of 400π cm3 . First, the cook…

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Q: An integral expression for the area of the surface generated by rotating the curve y=√x, 0≤x≤ 1…

A:

Q: What is the total change of f(x), if ƒ'(x) = 2x − 3x², over the interval [0, 3 -18 -12 -6

A: Given query is to find the total change for the given intererval.

Q: QuIf w=f(u, v) = cos uv, u = xyz ,v= 4(x²+y²) dw Prove that = 0 at the this point (x,y,z)=(1,1,1) дх

A: Given : w=f(u,v)=cos uv   , u=xyz ,v=54(x2+y2)   To Prove: ∂w∂x=0   at (x,y,z)=(1,1,1)

Q: 2. The value of O True O False ¹/² is = √13 13

A: