3x4+6x3-3x² - 6x + In 2-2x-In O x2−2x 2 -dx¹ (x-1) 1/6(x+2) 16/3 (x+1) 1/2 (x-1) 1/6(x+2) 16/3 (x+1) 1/2 (x-1) 1/6(x+2) 16/3 (x+1) 1/2 [ (x− 1) 1/6(x+2) 16/3 - x+1 O x² - 4x 2 O x²-4x 2 + In + In +C 0²] + C +C ) 16/3 ] + C

Q: (B) Find equations of the tangent and the normal lines to the curve y-exy = sinh x² +ln(x+√y point…

A: Given the curve y-exy=sinhx2+lnx+y at the point P0,1

Q: 22. Calculate the arc length of the graph of (a) y = f(x) = 1⁄2x³ + x-¹ over [1,3]. Hint: (b) y = 1…

A:

Q: The volume of the solid generated by revolving the region bounded by x²=4y and y2=4x about y=4 is to…

A: Given:  Region x2=4y             y=x24               y2=4x                y=4x                 y=2x…

Q: Suppose m and n are constants and m‡ n. 1. Evaluate sin(mx) cos(nx) dx

A: using trigonometric identity

Q: Question Find the area A of the region that is bounded between the curve f(x) = ex-2-3 and the line…

A:

Q: f(x) = x² + 5x - 1

A:

Q: For the function f(x) = 2x4 - 16x2 , find and identify any extrema (maximum/minimum) using the…

A:

Q: To integrate by u-substitution, which part of the integrand should you choose as u? S cos de sin² z…

A: We have to find out the substitution

Q: The solid bounded by the paraboloids 2= - 8+z²+ y² and z -3-32²-3y² has volume:

A:

Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

A:

Q: Compute the left and right Riemann sums L4 and R4, respectively for f(x) = √4x² on [-2, 2] and…

A: We can find Left and Right Riemann sums .

Q: 6. If f is continuous and f² f(x) dx = 6, evaluate S/² f (2 sin 0) cos de.

A: see below the answer and calculation

Q: S For x1/2 dx and using the substitution = x1/2, the resulting integral takes the form: x-x3 -du S-…

A:

Q: ³ SS ²0 Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,6,0), an

A:

Q: 28. 5x1 +4x2 2x1 2x1x2 - 2x3 = 4 + 3x3 = 2 + x3 = 1

A:

Q: Use Simpson's Rule to evaluate the following. n = 10 +3 1 dx J-3 1+x²

A: SOLUTION-

Q: QUESTION 15 Evaluate sin(Inx) dx Integration by parts will be used repeatedly. What is the…

A:

Q: Question 1 S x 1/2 dx and using the substitution = x 1/2, the resulting integral takes the form:…

A: The objective is to find the right option.

Q: The curves C1 and C2 are both symmetric with respect to the polar axis. Each of these curves is…

A:

Q: he definition of the derivative, find f'(x). Then find f'(-3), f'(0), and f'(4) when the derivative…

A:

Q: then what is y at x=1?

A: We can find y at x=1 in the following steps.

Q: Given: 3zxy Find fx O xy/3 O y/3 O x/3 None of the choices

A:

Q: b. Identify the function's local and absolute extreme values, if any, saying where they occur. -15…

A:

Q: Exercises To Solve [No.5] 3dx 9x²6x+5

A:

Q: ormulas to compute the following antiderivative. x-1 x² -dx.

A:

Q: ydx-xdy + xydy = 0

A: To solve the given ordinary differential equation problem.

Q: 4. Evaluate the following triple integral. [ƒÃƒ‚²‚x² sin y dy dz dx .

A:

Q: A wind is blowing giving the projectile the acceleration of 9m/s2 in the positive direction of the…

A:

Q: A payment of $2,690 was due two years ago, and a payment of $1,650 is due today. What single payment…

A: We have to solve for single payment.

Q: QUESTION 9 S x²-2x-In + In Evaluate 3x5 3x4+6x³-3x² - 6x O x2−2x 2 O x² - 4x O x² - 4x 2 て + In + In…

A: Solved below.

Q: If f(x) = 10, find f'(-1).

A: Given f(x)=10,  to find f'(-1) Formula used Differentiation of a constant value is zero d (constant)…

Q: = Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x)…

A:

Q: ng exercise, evaluate the integrals of the functions graphed using the formulas for a circles, and…

A: Topic:- geometry

Q: 5. Suppose f is continuous on [2, 8]. Use the table of values of f to f(x) dx using a left, right,…

A:

Q: Suppose the revenue from producing (and selling) x units of a product is given by R(x) = 8x-.01x²…

A: Marginal revenue at (x=30) =dRdxx=30

Q: QUESTION 6 Suppose m and n are constants and m‡n. Evaluate 1 1 -sin(m-n)x+ -sin (n m-n m+n n+n)x] +…

A:

Q: Find the area of the region that is bounded above by the curve f(x) = (x + 3)² and the line g(x) =…

A:

Q: Evaluate fun" (x) setx de Stan" 1 -tan (m + 1)(x) + — -tan (m-1)(x) + C m-1 ₁ (m + 2)(x) + -tan" (x)…

A: On solving this we will get Option (3) is correct

Q: Given the following pieces of information: I. a = (4, -2, 3) II. b = (0, 3, -5) Find: a) lal b) ab…

A: According to our guidelines, we can answer only one question or three subparts of a question. Other…

Q: Evaluate sin (Inx) dx Integration by parts will be used repeatedly. What is the expression after the…

A:

Q: Explain and sketch how a function can have f ''(a) = 0 at (a, f(a)) and not be an inflection point.

A:

Q: dx The integral (244) ² + A = cos²0 de B - sec ³0 de Ⓒ+√x³0 de Ⓒ÷-sin²0 D sin ²0 de can be…

A:

Q: 8 - 1V₁-30 √4 3+²+10 dt. Let g(x) = What is g'(x)? +4-3+²+10 322 3x² + 10 3x²+10 √8 O√TA 4+³ 6 2√14…

A: Topic = Derivative

Q: cos 3x cos 4x dx

A: ∫cos3xcos4xdx here we use formula  2cosxcosy = cos(x+y) +cos(x-y) here x = 4x      y = 3x

Q: 17. Evaluate the integral or show that it is divergent [(a)-(c)]. 4 6 14 dx (a) wzda, f (b) (b)dx,…

A: As per the instruction, we will be answering the first three subparts. For (a),…

Q: 2 I зах 9x²-6x+5

A: On solving this we will get

Q: 5. Evaluate the following triple integral. ſſſ (.x² + y² ) dx dy dz D D={(x,y):x² + y² ≤9.15:53)

A:

Q: Exercises To Solve [No.5] OS s dx (x-1) √x²2x-3 3-2x-x²

A: Explained below

Q: Question Find the area of the region that is bounded above by the curve f(x) = (x - 1)² and the line…

A:

Q: mx 13 if x < - 9 - Let f(x) = x² + 3x − 4 if x ≥ −9 If f(x) is a function which is continuous…

A: The objective of the question is determine the value of "m".