Use the Fundamental Theorem of Calculus to find the "area under curve" of f(x) = 6x + 15 between x = 4 and x = 7.

Q: Find x² - y²¹ lim (x,y) →(a,a) x² - y² O 2a O 2a² a² 00 DO

A:

Q: fin(1 + √x dx

A:

Q: Please help need asap..answer both please and i will rate high

A: We have to choose the correct option from the given options according to the given infinite series

Q: fxsinxdx O xcos(x) -In sin(x) + C ○ -xcos(x) + sin(x) + C O xcos(x) + sin(x) + C O xcos(x) - sin(x)…

A: Topic = Integration

Q: f3ex dx

A:

Q: Find an equation of the sphere with points P such that the distance from P to A(-2, 5, 2) is twice…

A: Let    P(x,y,z)  be the general point  A( -2, 5, 2)  and  B(6, 3, -3)PA=2PB Recall

Q: polar curves. 63. The complete circle r = a sin 0, where a > 0

A:

Q: Estimate the area under the graph of f(x) = rectangles and right endpoints. Rn = Repeat the…

A:

Q: Consider the function f(x) = 10√x + 4 on the interval [1, 8]. Find the average or mean slope of the…

A: Given the function is fx = 10x+4 on the interval 1, 8.

Q: Use the product rule to find the derivative of (4x⁹7x¹)(5e* - 4) Use e^x for e. You do not need to…

A:

Q: QUESTION 15 Use a graphing utility to graph the function over the indicated interval and approximate…

A: The answer as follows:

Q: Find the constants a and b such that the function is continuous on the entire real line. 7₁ ax+b,…

A:

Q: lim-(In(5n³-n+1)-in(7n³n+1)) 3 3

A:

Q: If the region occupied by a lamina is symmetric with respect to both the x- and y-axes, then the…

A: Solution: Consider the mass of the lamina ∫∫R ρ(x,y)dA

Q: If the sequence { 2 9 - An An - 3 converges to 6, then the sequence {an} converges to 9.

A:

Q: Explain why if a runner completes a 6.2-mi race in 33 min, then he must have been running at exactly…

A:

Q: Find the right match for the following ODEs in the dropdown menu y' = y" JS sin(x) 5xy' = y - 3x²y"…

A: This is a problem related to differential equation. Please find the answer as below.

Q: drawing the slope field for the differential equation , I would place slope lines of _________ at…

A: We have to find the required

Q: Find the power series representation of the function f(x) = = x 2x² +1'

A:

Q: The power series xn What is the power n! series representation of e(-²) ? ex is n=0 n=0 n=0 None of…

A:

Q: Express the complex number, 1 + ¿, in the form re¹ with 0≤0 < 2π. O √2e O √žeti ○ 2e Ti O eti O 2e7¹…

A:

Q: Consider the function f(x) = 3 - 3x² on the interval [-3, 6]. Find the average or mean slope of the…

A:

Q: Find parametric equations for the line. (Use the parameter t.) the line through the points (14, 3,…

A: Topic- Equation of line through given points

Q: 7. The value of a STOCK is modeled by the function : y = -40Cosx + 120 X=0 corresponds to January 1,…

A:

Q: Evaluate the following integral using trigonometric substitution. 7/2 1 0 dx 2 (4x²+1) ² What…

A: I have stated the used formulas in the solution

Q: Find the slope of the tangent line to the curve - 4x² - 2xy + 3y³ = | at the point (3, 1). - 33

A:

Q: In Prob. 1-38. Find dy/dx.

A: Given; y=e2x+3.

Q: Question Find the change in volume dV if a circular cylinder with radius r = 8 changes height from 7…

A:

Q: Use integration to find the area of the rose curve r = cos 20.

A: Area bounded by the polar curve Area=12∫ab r2 dθ

Q: Determine whether the following series converges. 5(-1)k+1 Σ k=1 k5 Let ak 20 represent the…

A: Given: Here,            ak=5-1k+1k5 and decreasing series.  Now,…

Q: Evaluate the following integral. Sxe 13x dx Let u=x². Use the integration by parts formula to set up…

A:

Q: Evaluate O |x + 1/² |x - 21³ O 3 ln x²-x2 + C In In In O In x+7 x²-x-2 ·S B +C |x+2/8/3 |x-1|5/3 |x…

A: This question can be solved using the concept of partial fraction.

Q: (c) Determine whether the series (2n)! Σ 7"-¹ (n!)² n=1 converges or diverges. (d) Show that series…

A:

Q: Solve the following initial-value problems starting from yo 6. dy dt A. - 7y y = At what time does y…

A:

Q: -0.001t² +0.6t, Suppose that in a memory experiment the rate of memorizing is given by M'(t) = where…

A:

Q: Find the general solution to the differential equation: y' = 8x + e²r

A:

Q: Consider the function f(t) = 4 sec² (t) — 8t². Let F(t) be the antiderivative of f(t) with F(0) = 0.…

A: find the integration?

Q: Given the equation below, find dy dx = Y dy dx - 17x² + 7x68y + y ¹⁰ = - 9 dy Now, use to find the…

A:

Q: Calculate the gradient, the divergence and the curl for the following fields, when possible: ₁ = e/y…

A:

Q: 23. The distance from a point (2, y) to the line 4x + 3y =0 is equal to 5. Find the value of y. O…

A: Given that the distance from a point 2,y to the line 4x+3y=0 isequal to 5. We need to find the value…

Q: SS. R (x² +. tyl JA 2 SS 1 0 277 2 2 (r² cos²o +r sine)r de dr It is left as an an integral exercise

A:

Q: Let r(t) = t²i + t cos(πt)j + sin(ät) k, find ſª r(t) dt.

A:

Q: Set up the double integral that solves for the area of the region that lies inside r = 3+2 cos θ and…

A: Given:          r=3+2cosθ , r=2

Q: [xcsc (y/x) - y]dx + xdy = 0 TEST FOR HOMOGENEITY OF DEGREE N: Let: F(x,y) = M(x,y)DX + N(x,y)dy…

A: The given differential equation is; [xcsc (y/x) - y]dx + xdy = 0

Q: Example 1 Find dy/dx, if a. y=sin(x² + 3x + 1) b. y = cos² (2x-1)

A: I have stated the used formulas in the solution

Q: Use integration to find the area of the rose curve r = cos 20.

A: Concept: Rose curve: A rose curve, commonly known as a multiform or Grandi's rose The rose's polar…

Q: Find lim (√2-t, et-¹, In(t + 1)) t-0

A:

Q: 50. y = 1/√; y(iv)

A: We can find the 4th derivative as below

Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.03 cm /…

A:

Q: Calculus

A: