Find the limit. lim X→x ←+ -54 -3 -2 -1 00 O-2 f(x) 00 SIEX) 4 m 2 14 -3 2 3

Q: For what values of a and b is the line 2x + y = b tangent to the curve y = ax² when x = 4?

A:

Q: 1. Find the second-order prediction error filter and the prediction error variance for the random…

A:

Q: Use the given conditions to write an equation for the line in point-slope form and slope-intercept…

A: We have to find out find slope form

Q: Consider the region depicted in the following figure. Find the area of R. -1 YA 4- 3+ 2 1 0 -1. f(x)…

A:

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) xy - 25 lim (x, y) → (5, 5)…

A:

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 (1) limx-o[: 1-cos x 2 sin²x (2)…

A: We have to find the limit using L Hospital rule.

Q: Evaluate the indefinite integral f7 sin v cos vdv =

A: Given ∫7sin6v cosv dvTo evaluate the integral:

Q: Evaluate the following integral. 45 S SS²² dz dx dy -411

A:

Q: Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. b…

A: We need to solve for the remaining angles and sides of the triangle.

Q: Given the following vector field and oriented curve C, evaluate F = (x,y) on the parabola r(t) =…

A:

Q: a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the…

A:

Q: (A): Solve the following linear equations by Cramer's rule: x + y + 2z = 1 2x-y-z = 0 x +2y-z = 4

A:

Q: S 2 (2 x ² + 1 ) 1²/1 2 dx

A:

Q: 8 If f(x) = 3 + = + x 6 x2 find f'(x). Find f'(4). Round to 3 decimal places if necessary.

A: Given that f(x)=3+8x+6x2-(i)Our Aim is to find f'(x) and f'(4).

Q: Find the general solution of the following differential equation. y" - 4y + 7y=0 NOTE: Use c₁ and c₂…

A: Given y''-4y'+7y=0

Q: f(a+h)-f(a) h a. Use the definition mtan = lim h→0 b. Determine an equation of the tangent line at…

A:

Q: 2 x²log₂ (x) dx S

A: Please show complete solution. (Use integration by parts)

Q: Evaluate the integral by applying the following theorems and the power rule appropriately. Suppose…

A: To find out the integration.

Q: Find the absolute maximum and absolute minimum values of f on the given interval. a)…

A:

Q: Suppose that a particle moves along a straight line with velocity v(t) = 10 - 1t, where 0 ≤ t ≤ 5.5…

A: Given: v(t)=10 -t, 0≤t≤5.5

Q: (C): Solve the following equations:- (1) sin 2x + 2 sin² = 1 (2) sech x - 4 tanh x = 1

A:

Q: Discuss the continuity of the function. 41 √x² + y² + z² f(x, y, z) == continuous except where x² +…

A: The given function,   fx,y,z=41x2+y2+z2

Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…

A:

Q: Find the volume of a solid of revolution formed by revolving the region bounded by the graphs of…

A:

Q: Think back to early in the semester when the weather was cold and often snowy. Imagine that in a…

A: Concept: Here we have the height of the mound is 24 inches (h) And the base of the mound is 36…

Q: cise (a) e volume of the solid formed by revolving the region about the x-axis 01 he region is…

A: To find the volume of solid revolving around x axis using disk method

Q: 10. After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A: Sol:- To find the maximum concentration:-

Q: Evaluate the indefinite integral as a power series , x² ln(1 + x)

A: We want to find the indefinite integral as a power series.

Q: 12 - y+ ] - dy = |+C

A:

Q: Find the distance between the pair of points (2.5,8.2) and (-0.5,5.2). If necessary, express the…

A:

Q: 4. y = Ae bx are cosax + Bebx sinax, where a and b(lowercase) parameters. (not to be eliminated)

A:

Q: Q5: Find dx (1) In(x - y) = xy + y² : (4) y = x sinh 2x-cosh 2x for the following functions: (2) y =…

A:

Q: Consider lim (x,y) → (0, 0) xy 20 X (see figure). 20 20 (a) Determine (if possible) the limit along…

A: Here to determine, lim(x,y)→(0,0)x2+y2xy

Q: (B): Find the unit vector 3i - 4j + 5k perpendicular to the vectors: 4i + 5j-6k

A:

Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j+5k 4i + 5j-6k ;

A:

Q: e (5-x) dx = xydy

A:

Q: Use the figure below to find the exact value of the trigonometric function of angle A. sin (A) 6 A…

A: it is very basic question of trigonometry.

Q: (B): If A = 2i + 3j - 4k; B = 3i - 4j + 5k and C = i + j - k, find: (ii)B.C (iii)A. (B+C)and (A+B).C…

A:

Q: 34. dx = x³+4x² + 5x - 1 is given. What is ƒ(1)? A.-7 B.3 C.-2 D. 16 35. Evaluate the integral f(x²…

A: 34) The integration of the integral is f(x)/x2=x3+4x2+5x-1.  35) The given integral is…

Q: [² 11. [(2 sinx+cos.x) dx 9. 13. 15. x¹/3 19. 21. 3 x2/3 - dx 17. [(3 cos x - 2) dx [(5x- 2²/1) dx…

A: Disclaimer:  “Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find the radius of convergence, R, and the interval of convergence, I, of the following series.

A: The given series: ∑n=2∞x+2n2n ln n

Q: Use the method of reduction of order to find a second solution of the differential equation t²y"…

A:

Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

A: I have stated the used formulas in the solution

Q: S 2 (2x² + 1) dx

A:

Q: xdx x²+6x+18 7. f cos(lnx)dx 8. fest sin(at) dt 6. f

A:

Q: Set-up and evaluate the triple integral for the mass of the box 1≤x≤2, 1≤y≤16, 0≤z≤ with √√y density…

A: To setup and evaluate the triple integral for mass of the box.

Q: Find both first partial derivatives. z=(4 xy)/(x^2+y^2) fx(x,y)= fy(x,y)=

A:

Q: If A, B, and C are 3×3 matrices; and det(A) = 5, det(B) = −2, and det(C) = 3 then compute: det…

A:

Q: 12. (2xy³ + 1) dx + (3x²y²-y¹) dy = 0

A:

Q: Find all the values of x such that the given series would converge. (x-8)" 8n n=1 The series is…

A: We will use ratio test.