(a) Give the linearization L(x) of f(x) at x = 2. (b) Use your answer from Part (a) to estimate the value of ƒ(2.1). (c) Suppose you are told that ƒ"(2) < 0. Does this lead you to believe that your estimate in Part (b) is too high or too low? Explain.

Q: Question 2 Find a differential equation whose general solution is y = c₁est + c₂e-2t. 0 2

A:

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

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. / (1 + 3x) dx 5 2. / u² (4 + u°) ³ du

A:

Q: The graph of y = f(x) is shown. Use the graph to answer the question. Find lim x-(-1)- O-2, -7 O-7,…

A:

Q: Let h(x)=f(x)g(x) where f(x)=−3x2+4x−1 and g(x)=−x2+4x+3. What is h′(4)? Do not include "h′(4)=" in…

A:

Q: The marginal cost for printing a paperback book at a small publishing company is c(p) = $0.012 per…

A: Given data÷ Marginal cost  cp=$0.012 per page  Where p=number of pages

Q: A particle moves along a line with a velocity v(t) = -2t+4, measured in meters per second. Find the…

A:

Q: g(x) dx = (Simplify your answer.) 7 4g(x)dx= 2 (Simplify your answer.) 7 [g(x)-f(x)]dx = (Simplify…

A:

Q: Suppose that over a certain region of space the electrical potential V is given by the following…

A:

Q: Q3/ A. For the following function f(x). Find: i. iii. f(x) = x² + 1 The slope of the f(x) by using…

A: We need to find out the slope using the definition.

Q: Graph the function and the indicated tangent line. Graph f(x) = -4x2 and the tangent line to the…

A:

Q: Q5: Find for the following functions: (1) In(x - y) = xy + y³ (2)y=tan³ √/cot(7x); (4) y = x sinh…

A: Solution is given below:

Q: 0²1' (19²¹) = (1) 1

A:

Q: Find the cross products uxv and vxu for the the vectors u=2i-j-2k and v= i +3j-2k.

A:

Q: Suppose that f is integrable on [-4, 7]. If the average of f on the interval [-4, 7] is 4.25, fin 4…

A:

Q: Determine whether the improper integral diverges or converges. 16 1 √√√x dx converges diverges…

A:

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: Q2: Find the 1. y = 1- 2. y [In(x² + 2)²]³ 3. y = xcsex tan² (cos x) 4. y for the following…

A: As per guidelines we can answer only one question at a time, so if you need more answers kindly…

Q: Q2: Solve the following int (1) dx 1 (x+3)(x+7)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: dw (C): If w = tan x and x = 4t³ + t ; Find dt

A:

Q: Solve the following differential equations: (1+x²) (dy-dx)=2xy dx

A:

Q: y = sin(x), y = 0, x = 0, x = Exercise (a) the volume of the solid formed by revolving the region…

A:

Q: what is under the 15872 is that a 9

A: The given integral,   ∫-44∫15∫1ex2y2zdz dx dy

Q: The figure to the right shows four regions bounded by the graph of y=x sinx: R₁, R₂, R3, and R4,…

A:

Q: Transform the given differential equation into an equivalent system of first-order differential…

A: Using substitution and differentiation,

Q: Find the limit. lim (x,y) → (5, 1) ety Discuss the continuity of the function. O continuous…

A: See this solution in below

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

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

Q: 2: Solve the following integrals: - 7x² +14x+15 (x²+3)(x+7) dx ; 1) S

A: Given: ∫7x2+14x+15x2+3x+7dx

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: Q5: Find for the following functions: dy dx (1) In(x - y) = xy + y² ;

A: Find the derivative

Q: Q4: Answer two only: 4 2 2 1 -1 1 (A): If A = -2 Find AB and AC. 01 0; 2 B = 2 -1 3 -2 -2 and 2 1 3…

A:

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

A:

Q: Q3: Evaluate the following integrate: (chose three only) 1. dx 1+x4 2. ex-edx ex+e-x 3. fxsec² x dx…

A:

Q: Discuss the continuity of the function. f(x, y, z)= sin(z) ex + ex continuous except at (0, 0, 0)…

A: Our Aim is to discuss the continuity of the function given below:-f(x,y,z)=sin (z)ex+ey -(i)

Q: of x³ (4+x²)² dx ; Use rationalizing substitution

A:

Q: Find the lengths of the sides of an isosceles triangle with a given perimeter if its area is to be…

A: Solution is given below:

Q: + 2 .4 i ti ti ti ti + i _ ។ { / - 1 "

A:

Q: Use the figure below to find the exact value of the trigonometric run tan(A) 7 A

A: The solution is given below

Q: Simplify the following with out 1) -5, 3+1 using the denominator

A:

Q: • The orthogonal trajectory of the equation given below is already given. What is the value of "n"?…

A: The given equation x2+3y2=r2

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

A: 3 1) limx-0[1/(1-cosx) -2/sin2x ] 2) limx-0 (tan-1x-x) x-3

Q: Match the graph of the surface with one of the contour maps. f(x, y) = e¹-x² - y² O O X x

A: Given that       f(x,y) = e1-x^2-y^2

Q: Q2: Solve the following integrals: (1) f 7x²+14x+15 (x²+3)(x+7) dx ; (2) f sin x+cos x dx sin³ x…

A: We will use partial fraction to solve the first part of the question.

Q: Skill Building In Problems 13-24, use the graph on the right of the function f. 13. Is fincreasing…

A: Please see the answers below.

Q: (C): If w = tan x and x = 4²³ +t: Find?

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: Solve the following differential equations: a- (2x + 3y -2) dx + (3x -4 y +1) dy=0 b- (x²+3y²)…

A: The given differential equations are;  1) (2x+3y-2)dx+(3x-4y+1)dy=0 2) (x2+3y2)dx-2xydy=0.

Q: Find the average rate of change of the function f(x) = x² + 3x from x₁ = 2 to x₂ = 4. The average…

A: The function f(x)=x2+3x from x1=2 to x2=4

Q: Sketch the plane curve. r(t) = 3ti - tj, [0, 3] y O 2 1 -1 -2 y 3 2 - -1 -2 2 4 4 Find its length…

A: This question is related to vectors and parametric equations, we will solve it using given…

Q: Find the Taylor or McLaurin series for the following functions f(x) = ln(1+x), a = 0

A: According to the question we need to find out the McLaurin series.