By the alternating series test, the series First find the partial fraction decomposition of 7 k(k+10) Then find the limit of the partial sums. 8 7(-1) ²+1 k(k+10) k=1 Enter your answer for the sum as a reduced fraction. = 7(-1) k(k+ 10) k=1 7 k(k+10) = converges. Find its sum.

Q: Find a Cartesian equation for the curve. r = 7 sec (0) Identify the curve. O circle O hyperbola O…

A:

Q: 7/21/22, 1:51 PM 8. Find the indefinite integral. Check your work by differentiation. -x) dx 8x(7-x)…

A:

Q: Evaluate the integral. Show that the substitution x = √14 sec (0) transforms I into cos(0) dº, and…

A:

Q: Find the local linear approximation of g(x) = e-*sinh() at x = 0 and use it to estimate the value of…

A: To find the local linear approximation of gx=e-x sinhx2 at x=0  and by using it to estimate the…

Q: Find the scalar and vector projections of b onto a. a=3i-j+4k, b=j+k

A:

Q: A 10-kg quantity of a radioactive isotope decays to 7 kg after 17 years. Find the decay constant of…

A:

Q: 7. f(x)=√x, √√x, a = 1

A:

Q: Find all real solutions of the equation by first factoring the left hand side and then taking a…

A: x2+10x+25=25⇒x2+10x+25-25=0⇒x2+10x=0

Q: Write an equation for the polynomial graphed below Af y(x) = 42

A: Given graph of polynomial has x intercepts -4,-2 and 1 and double root is 4 Y intercepts is -2.

Q: 4. Perform the line integral F. dr, where the vector field is F(x, y) = yi+xj, and the path C is…

A: Fundamental of line integral ∫F.dr = ∫t1t2F( r )r'( t )dt Given F( x , y ) = yi + xj r( t ) = cost i…

Q: Find h'(t) given:h(t) = - 4.9t2

A:

Q: Graph the polar equation of a parabola. 8 1- cos 0 r=

A: Consider the polar equation  r=81-cosθ

Q: Given the vector u equal to 6 (cos 205°, sin 205°) and vector v equal to 5 (cos 120°, sin 120°),…

A:

Q: ? Exercise 14.5.2 дz Az To calculate and for the following functions: Ju дv first calculate: Oz Ax…

A:

Q: 43. y = (4 — x²/3)³/2, [0,8] -

A:

Q: Find the distance between the two parallel planes 5x3y + z2=0 -10x + 6y2z+3=0

A:

Q: [ ,20 ' sin (30 ) d0

A:

Q: Given vectors u =(−3, 2) and v = (6, 7), find the sum u + v and write the result in component form.

A:

Q: 04: Find x and y which satisfy the relation: -4 XZ ×-- ]

A:

Q: The population of a certain state was 10,290,518 in 1945 and 23,626,378 in 1990. a. Assuming the…

A:

Q: aph the function. Then use your graph to find the indicated limit. 3) f(x) = 7ex, lim f(x) x-0 Îy H…

A: The given function is fx=7ex

Q: ㅠ Let D be an ellipse rotated counterclockwise by radians, as pictured below. Before rotation, the 6…

A:

Q: 10. Use Euler's method with h = 0.1 to approximate the solution to the initial value problem y=x-y,…

A:

Q: Solve for x: log₂ (2¹) --4 2

A: This is question of calculus Here one logerithmic equation given we have to solve for it. Further…

Q: Calculate the iterated integral. 64 8 [** [* (* + X) Jv dx dy

A: Double integral.

Q: Find the length of the graph of f(x) - + 1 1≤ x ≤4

A:

Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region…

A: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region…

Q: Evaluate lim f(x) and lim f(x) for the rational function. Then give the horizontal asymptote of f…

A: f(x)=28x6-84x6-5x5

Q: Find the Taylor polynomial T₂(x) for the function f(x) = 6e²x at x = 0. (Use symbolic notation and…

A:

Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

A:

Q: Evaluate the following limit. Enter the exact answer in fraction form, if necessary. To enter ∞ in…

A: let B=limx→∞(5x159x13+31x15)

Q: 1. Perform the double integration: and r = y³ in the first quadrant. 1 SS₁ (²- (x - y) dA, where D…

A: given double integration ∫∫D(x-y) dA where d is the region in the x-y plane bounded by y=x3 and x=y3…

Q: Sketch the curve with the given polar equation by first sketching the graph of r as a function of 8…

A: r2θ=49 To sketch the curve, we can start by graphing r as a function of theta in Cartesian…

Q: Find the indefinite integral using the substitution x = 3 sin(0). (Remember to use absolute values…

A: The given integral is: ∫9-x2x dx

Q: Find the Elasticity of Demand at a price of $28

A:

Q: An √n²-1-√√n²+n

A: an=1n2-1-n2+n

Q: Use partial fractions to find the indefinite integral. (Remember to use absolute values where…

A:

Q: 7. The integral in this exercise converges. Evaluate the integral without using a table. 2 2 İ DO 1…

A:

Q: 2 Solve the inequality f(x) <0, where f(x) = x²(x-4), by using the graph of the function. Q -~ EN…

A: To solve the following problem

Q: What is an equation for the cosine graph shown below?

A:

Q: 2. Use the product rule to find the derivative for g(x)= (3x*-7)(2 - 5x³) and create the equation of…

A:

Q: Determine whether the series is convergent or divergent by expressing s as a telescoping sum. If it…

A: To find the series is convergent or divergent if convergent  then find the sum of series.

Q: Evaluate the limit. x-1 lim x 1 √√x-1

A: given limits limx→ 1x-1x-1

Q: Form a polynomial whose real zeros and degree are given. Zeros: -2,0, 8; degree: 3 Type a polynomial…

A:

Q: Which of the following does not provide the exact value of the instantaneous rate of change at x=a?…

A: The instantaneous rate of change of a function f(x) at a point x=a is the derivative of the function…

Q: Given the demand function D(p)=√150 - 4p, Find the Elasticity of Demand at a price of $6 At this…

A:

Q: How did you choose pi/2, -pi/2 when setting it equal to 3 theta.

A: How did you choose : 3θ = π/2 and –π/2

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(p,…

A:

Q: Use the functions given by f(x) = x + 4 O-43√x +4 O-43√x-4 ○ 43√x-4 43√x + 4 1 64 -x 4 and g(x) = x³…

A:

Q: Calculate the arc length of y=x²-½ln(x) c over the interval [1, 2e]. (Use decimal notation. Give…

A: