Exercises: Use the theorems on limits to evaluate each of the following, if it exists. 1. lim (2x³ 4x² + 5x - 10) x-1 2. lim X-3 x²-4 9x²-16 4x²+4x+1 x-1/2 2x²-x-1 3. lim 4. lim - x-2 x-2x²-3x+2 x³+1 5. lim X→1 x+1 x²+1 x-5 √2x+2-2 |x-2| X-2 X+2 6. lim 7. lim x³+27 x-3 x²-9 8. lim 9. lim √6-x-x x-2 x²-4 10. lim X-5 √x²+5-√30 x-5

Q: Find the average value fave of f(x) = x³ between -1 and 1, then find a number c in [-1,1] where f(c)…

A:

Q: e cos(x) = 1 + sin(xy) 2 2

A:

Q: Evaluate the integral by making the given substitution. [sec (3x)tan (3x)da, u = 3x +C

A:

Q: Find the complete solution of the linear system, or show that it is inconsistent. (If the system has…

A: The objective of the question is determine the solution of the system of equations.

Q: (2x+5)³(52²-2x) 4. Use logarithmic differentiation to find the derivative of the function y = √2x+5

A:

Q: Find foda + C

A:

Q: All of the following represent a shape or region in 3D space. A subscript 0 means the symbol is a…

A: The three coordinates (r, θ, z) of a point P are defined as: The axial distance or radial distance…

Q: Write a limit using summations that would equal 0 tan (2x) dx.

A:

Q: 2. The piecewise function g(x) is defined as follows (x+2)³ g(x) = cos(x) (x-1)²/2 if x 1. (a)…

A: Please see the below picture for detailed solution.

Q: dx 3 sin x-6 cos x

A:

Q: (3x - 2y + 1) dx + (3x - 2y + 3) dy = 0.

A:

Q: Find the derivative of y with respect to x in the following equation.

A: Using chain rule of differentiation

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = ln(x + 5y + 6z). F(x, y, z) = =

A:

Q: 2 x 0 2x+53 +18x+130 -dx

A: In this question we have to solve the given Integral.∫012x+53x2+18x+130dx

Q: c. A ball is shot from the ground straight up into the air with initial velocity of 49 ft/sec.…

A:

Q: Let f be the function graphed below. If 20 subintervals of equal length are used, write a summation…

A:

Q: 3. Below is the graph of f '(x), the derivative of f(x), and has x-intercepts at x = -3, x = 1 and x…

A: Topic- application of derivatives

Q: 6) 3/2 · 4x²)³/; 9x dx

A: Our Aim is to solve the integral given below:-∫9-4x252x6dx -(i)

Q: Find the indicated value. f(5,2) if f(x,y)=2x²y-5xy³ f (5,2)= 10 (Type an integer or a simplified…

A: Given a function fx,y=2x2y-5xy3 We have find the value of fx5,2 Derivative of a polynomial function…

Q: Solve the differential equation (2x + y) dx - O a. 5x+10y + In |10x O b. O c. 5x O d. 5x (4x + 2y -…

A:

Q: Find the area S of the shaded region in the figure if ƒ (0) = 0² + 30. Note that 0 varies from 0 to…

A: To find the are S of the shaded region in the figure if fθ=θ2+3θ Note that θ varies from 0 to…

Q: Find the Taylor series generated by f(x) = 6 sin 5 at x = 0.

A: Answer is in next step.

Q: The area of a square is increasing at a rate of 56 centimeters squared per second. Find the rate of…

A: Given data÷ Rate of change of area  =dAdt=56cm2/s Side of square =a=4cm We need to find dadt=?

Q: 3x³-28x² +40x-42 3x² - 4x+5 dx

A:

Q: 5. The movement of the crest of a wave is modelled with the function h(t) = 0.2 cos(4t) + 0.3…

A:

Q: Let à = (1, -2, 0) and 6 = (1, 3,2). b Find the angle between the vector (in radians) Check Answer

A:

Q: Solve the differential equation [x a. b. C. d. y tan ¹()] 2x tan-¹(²) -¹ (²/2) dx + x tan¯¹ (²/2)dy…

A:

Q: Determine the real number a such that u x v and i are orthogonal, where u = 5i + j - 9k and v = 6i -…

A:

Q: Q4. Find the values of the constants a, b, c so that - F = (axy + bz³)ī+ (3x² − cz)j + (3xz² − y)k…

A:

Q: A tank half-filled with water is in the form of a rectangular parallel piped 5ft deep, 15 ft wide…

A: Answer is c

Q: Show that (u₁. U₂. u) is an orthogonal basis for R³. Then express x as a linear combination of the…

A: Answer is in next step. please give a like !!

Q: m M|L II k=0 CO M« Σ N சிய

A:

Q: 2. A force F = [-2,1,5] in Newtons, pulls a sled through a displacement s = [-3, 5, 4] in metres.…

A: Using dot product of vectors and obtain the magnitude of the force vector

Q: Find the integral of f(x) = 1 √1-16x² between 0 and 1.

A: The given integral is 1/sqrt(1-16x2).

Q: Find the particular solution of the following second order differential equation d² y dy dx² --4-…

A: The given differential equation is :d2ydx2-4dydx-21y=-105x-209given that y0=11 ; y'0=39.

Q: Determine whether the following vector field is conservative on R³. If so, determine the potential…

A:

Q: Differentiate the following function. You do not need to simplify the derivative. ƒ'(x) = 5 f(x) =…

A: Derivative of function f(x)=lnx5

Q: Consider the function f(t) = 10 sec² (t) - 3t³. Let F(t) be the antiderivative of f(t) with F(0)…

A:

Q: -5-4-3-2 Ob Oa Oc Od 1.- 1 -1- -2 -3- y 3 24 1 12 Check Answer 345 +4-3 -5-4-3-2 243 116,536 1 -1-…

A:

Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

A: Given figure  with areas Now V=∫010f(x)dxV=∫03f(x)dx+∫35f(x)dx+∫57f(x)dx+∫710f(x)dx

Q: S dx 3 cos x-2 sinx+3

A:

Q: In the figure, the regions A, B, C and D bounded by the x-axis and the graph of f have the following…

A: Here we will find the definite integral,

Q: Let à = (-5, 4, Find the projection proja b =< 4) and b = (-4, 0, -1). of b onto a. -

A:

Q: 2x lim(x,y)→(0,0) x² + x + y²

A:

Q: Let r(t) = (-5t5 - 3, 4e-4t, 5 sin(2t)) - Find the unit tangent vector T (t) at the point t = 0.…

A: Given vector  r(t)→=&lt;-5t5-3,4e-4t,-5sin(2t)&gt;

Q: A sequence is defined recursively by the given formulas. Find the first five terms of the sequence.…

A:

Q: Use cylindrical coordinates to integrate f(x, y, z) = z over the intersection (i.e. all the volume…

A:

Q: S √x²-a² X dx

A: To solve the given integral.

Q: 1 2 ¹/² (²1-5) dz. Write a limit using summations that would equal

A:

Q: Find the area under the curve y Т over the interval [1,4]

A: Topic = Area