² fx ds, where C is с t a. the straight line segment x = t. y = from (0,0) to (16,4) b. the parabolic curve x=t, y = 3t², from (0,0) to (1,3) a. For the straight line segment, x ds = (Type an exact answer.) Evaluate

Q: Find the critical number of the function defined by f(x) = x² + 4x O-1 and 0 are the critical…

A:

Q: Using trigonometric substitution to evaluate: The first thing we'll need to do here is complete the…

A:

Q: 10. Find the area of the paraboloid x² + y + z² = 2 by the plane y = 0. (Hint: Implicit Surface)

A:

Q: Using Disk Method solution, R is bounded by x-axis, y-axis and the line 2x + 3y = 1. This is…

A:

Q: Calculate the first five derivatives of f(x) = sin(x). Then determine f(24) and f(25). (Use symbolic…

A:

Q: f sin √x dx

A:

Q: 7 (t) = (4t³, 5t²). Find 7 '(t).

A:

Q: Determine whether each of the following series converges. (Make sure to state which test you are…

A:

Q: The Bernoulli's form of the differential equation xdy - [y + xy³ (1 + ln x)]dx = 0 is

A:

Q: Solve the differential equation y Pemer 6a y5 subject to the condition that y 3 when = 3.

A: Here we have to solve the given differential equation

Q: The edge of a cube was found to be 20 cm with a possible error in measurement of 0.2 cm. Use…

A: Differential

Q: 3. In evaluating the integral S fractions. Let x² dx (x-1)²(x²+1)' you will decompose x² dx…

A:

Q: Evaluate the given surface integral a) ff x² ds where S is the unit sphere: x² + y² + z² = 1 b) ff…

A:

Q: Find T(t) and N(t) at the given point. r(t) = 7 cos(t)i + 7 sin(t)j; t = 3 T() 3 N(₁) 3. =

A: Given, r(t)= 7cos(t)i+7sin(t)j We know that,…

Q: Using trigonometric substitution to evaluate: The first thing we'll need to do here is complete the…

A: To find  after completing the square  what will be the obtained polynomial.

Q: In(a³6³) (c) In(be)² a (d) (In c³) (In 62 -4

A:

Q: Let f(x)=√x - 3 on [4, 12]. Find all numbers c in [4, 12] for which the derivative is equal to the…

A:

Q: 2(-3x+1), dx

A: I=∫ 32(-3x+1) 2-3x dx21-3x =t21-3x ln2  ddx(1-3x) dx=dt-3 ln(2) 21-3x dx=dt2-3x dx=dt-6 ln 2

Q: For a non-negative function f(x), an approximating formula for the area under curve using a uniform…

A: The area approximation formula is Area≈∑fci∆xi=1n. Where fci=Height of the ith rectangle   ci…

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: r(t)=cos(πt) i -ln(t) j+t-12 kDomain of:cos(πt): no restrictions.(-∞, ∞)-ln(t): defiend for…

Q: 6.S dx √1+√√x

A:

Q: The heights on the graph of f'(x) correspond to the slopes of the lines tangent to the graph of f.…

A:

Q: 3. The Bernoulli's form of the differential equation x' ydx+(3x-y'dy=0 is

A:

Q: Sketch the region enclosed by the curves à - 5 = 4y and x − 21 = (y — 4)², and compute its area.

A: x-5=4y⇒x=4y+5     x-21=(y-4)2 ⇒x=(y-4)2+21 Area between the curves…

Q: Find the arc length of the graph of NOTE: Enter the exact answer. L || r(t) = √²ti + e-√²tj + 2tk,…

A:

Q: the

A:

Q: Find the derivative of y = log2 4x Ox/In4 O 1/xln4 O4/1n4 @ 4/xin4

A: To solve the following problem

Q: The angle below subtends an arc length of 5.52 cm along the circle centered at the angle's vertex…

A: We know that θ=lr⇒θ=5.522.3=2.4 radians.

Q: (y² +1)dx +(2xy+1)dy

A: (y2+1)dx+(2xy+1)dy=0  It is of the form Mdx+Ndy=0whereM=y2+1N=2xy+1Then ∂M∂y=2y       ∂N∂x=2ysince…

Q: Evaluate the definite integral. NOTE: Enter the exact answer. 12 ti + t²idt = 0

A: To evaluate: ∫012t i+t2jdt

Q: Points A and B are separated by a lake. To find the distance between them, a surveyor locates a…

A:

Q: An angle's initial ray points in the 3-o'clock direction and the angle measures 0.48 radians. A…

A:

Q: * Using trigonometric substitution to evaluate: find dx √ dx, √2x²-4x-7 (3√2)/2 cosø dø O (3√2)/2…

A:

Q: Non-Exact H.W: (2xy ey+2xy³+y)dx + (x²y^ey-x'y-3x)dy=0

A:

Q: Construct the truth table for each of these compound propositions: a. (pvq) → (p @q) b. (p^q) → (pv…

A: We have to find the truth table for the given compounded prepositions.

Q: Verity Green's Theorem by evaluating both integrals ƏN [x² dx + x² αy = [] (2 - 0) A √y² dy dA ax ду…

A:

Q: dx Find given that dt 6x² + 7y² = 13 x = 1, y = -1, and Give your answer as a simple fraction. dx dt…

A: Let us consider an expression, ax+by=c , a,b,c are constants. Then by implicit differentiation on…

Q: s dx x+√2x+1

A: Let  2x+1=u ⇒dudx=12x+1 ⇒dx=2x+1du also x=u2-12  ∫dxx+2x+1=2∫uu2+2u-1du…

Q: Teddy got 87% in his Quarterly Assessment for Physical Education and Health. If there are 65…

A: Teddy got 87% in his Quarterly Assessment for Physical Education and Health. If there are 65…

Q: Step 4 Thus, (x x cos(8x) dx =

A: To solve the following problem

Q: One historic earthquake had magnitude of 8.9 on the Riteter scale. How that had a magnitude of 8.5?…

A: Given:       If I1 and I2 are two intensities, then we are required to find I1I2. To relate this to…

Q: (5) Please help me answer this one. Read the problem and questions very carefully. Show your…

A: This is a problem related to percentage part of the mathematics. Based on the general formula and…

Q: Consider the following. C: line segments from (0, 1) to (0, 16) and (0, 16) to (15, 15) (a) Find a…

A:

Q: S 7 tan (2x) dx 2 Hint: tan²x = sec ² x - 1

A:

Q: 3. Sketch the graph of y=-2 sin Show evidence of transformations. Clearly plot your points. y=-2 sin…

A: Given:       y=-2sin2θ-π3+4  This is in the form of y=asinbθ-c+d       Here a=-2                b=2…

Q: Consider the following series. Σ» (#1) (a) Determine whether the series is convergent or divergent…

A:

Q: 3. In evaluating the integral ſ x²dx (x-1)²(x²+1)' you will decompose x²dx (x-1)²(x²+1) into simpler…

A:

Q: Find the limit. lim (ti – 4 · 4 j + t² k) t→7 lim (t i − 4 j + t² k) = i 1→7 i+ i j+ i k

A:

Q: Evaluate the definite integral. NOTE: Enter the exact answer. So||ti + Bij||dat 1717- = 13 X

A:

Q: Determine whether the series is convergent or divergent. arctan 2n n = 1 O convergent O divergent If…

A: