Sách Toán – Học Toán – Đề Thi Toán https://booktoan.com Học toán, Đề thi toán, Sách giáo khoa Toán, trắc nghiệm Toán online Wed, 17 Mar 2021 14:16:29 +0000 vi hourly 1 https://wordpress.org/?v=7.1.3 Cho hàm số \(f\left( x \right)\) liên tục trên \(\mathbb{R}\), thỏa mãn \(f\left( x \right) = x\left( {1 + \frac{1}{{\sqrt x }} – f’\left( x \right)} \right)\,,\,\forall x \in \left( {0\,; + \infty } \right)\) và\(f\left( 4 \right) = \frac{4}{3}\). Giá trị của\(\int\limits_1^4 {\left( {{x^2} – 1} \right)f’\left( x \right){\rm{d}}x} \) bằng https://booktoan.com/cho-ham-so-fleft-x-right-lien-tuc-tren-mathbbr-thoa-man-fleft-x-right-xleft-1-frac1sqrt-x-fleft-x-right-rightforall-x-in-left-0-infty.html https://booktoan.com/cho-ham-so-fleft-x-right-lien-tuc-tren-mathbbr-thoa-man-fleft-x-right-xleft-1-frac1sqrt-x-fleft-x-right-rightforall-x-in-left-0-infty.html#respond Wed, 17 Mar 2021 14:16:29 +0000 https://booktoan.com/?p=174843 https://booktoan.com/cho-ham-so-fleft-x-right-lien-tuc-tren-mathbbr-thoa-man-fleft-x-right-xleft-1-frac1sqrt-x-fleft-x-right-rightforall-x-in-left-0-infty.html/feed 0 Câu 48: (MH Toan 2020) Cho hàm số $f(x)$ liên tục trên $\mathbb{R}$ thỏa mãn $xf\left( {{x}^{3}} \right)+f\left( 1-{{x}^{2}} \right)=-{{x}^{10}}+{{x}^{6}}-2x$, $\forall x\in\mathbb{R}$. Khi đó $\displaystyle\int^0_{-1}f(x)\mathrm{d}x$ bằng https://booktoan.com/cau-48-mh-toan-2020-cho-ham-so-fx-lien-tuc-tren-mathbbr-thoa-man-xfleft-x3-rightfleft-1-x2-right-x10x6-2x-forall-xinmathbbr-khi-do.html https://booktoan.com/cau-48-mh-toan-2020-cho-ham-so-fx-lien-tuc-tren-mathbbr-thoa-man-xfleft-x3-rightfleft-1-x2-right-x10x6-2x-forall-xinmathbbr-khi-do.html#respond Tue, 07 Apr 2020 21:12:44 +0000 https://booktoan.com/cau-48-mh-toan-2020-cho-ham-so-fx-lien-tuc-tren-mathbbr-thoa-man-xfleft-x3-rightfleft-1-x2-right-x10x6-2x-forall-xinmathbbr-khi-do.html https://booktoan.com/cau-48-mh-toan-2020-cho-ham-so-fx-lien-tuc-tren-mathbbr-thoa-man-xfleft-x3-rightfleft-1-x2-right-x10x6-2x-forall-xinmathbbr-khi-do.html/feed 0 Câu 38: (MH Toan 2020) Cho hàm số \(f(x)\) có \(f(3) = 3\) và \(f\prime (x) = \frac{x}{{x + 1 – \sqrt {x + 1} }}\), \(\forall x > 0\). Khi đó \(\int\limits_3^8 f (x){\rm{d}}x\) bằng https://booktoan.com/cau-38-mh-toan-2020-cho-ham-so-fx-co-f3-3-va-fprime-x-fracxx-1-sqrt-x-1-forall-x-0-khi-do-intlimits_38-f-xrmdx-bang.html https://booktoan.com/cau-38-mh-toan-2020-cho-ham-so-fx-co-f3-3-va-fprime-x-fracxx-1-sqrt-x-1-forall-x-0-khi-do-intlimits_38-f-xrmdx-bang.html#respond Mon, 06 Apr 2020 11:47:19 +0000 https://booktoan.com/?p=172940 0\). Khi đó \(\int\limits_3^8 f (x){\rm{d}}x\) bằng A. \(7\). B. \(\frac{{197}}{6}\). C. \(\frac{{29}}{2}\). D. \(\frac{{181}}{6}\). LỜI GIẢI Đáp án: B Ta có: \(f(x) = \int f […]]]> https://booktoan.com/cau-38-mh-toan-2020-cho-ham-so-fx-co-f3-3-va-fprime-x-fracxx-1-sqrt-x-1-forall-x-0-khi-do-intlimits_38-f-xrmdx-bang.html/feed 0 Xét hàm số $ y=f\left( x \right)$ liên tục trên đoạn $\left[ -1;2 \right]$ và thỏa $ f\left( x \right)=\sqrt{2+x}+x.f\left( 3-x^2 \right)$. Tính $I=\displaystyle\int_{-1}^2{f\left( x \right)\textrm{ d}x}$. https://booktoan.com/xet-ham-so-yfleft-x-right-lien-tuc-tren-doan-left-12-right-va-thoa-fleft-x-rightsqrt2xx-fleft-3-x2-right-tinh-idisplaystyleint_-12fleft-x-righttextrm-d.html https://booktoan.com/xet-ham-so-yfleft-x-right-lien-tuc-tren-doan-left-12-right-va-thoa-fleft-x-rightsqrt2xx-fleft-3-x2-right-tinh-idisplaystyleint_-12fleft-x-righttextrm-d.html#respond Fri, 13 Mar 2020 00:10:31 +0000 https://booktoan.com/?p=172172 https://booktoan.com/xet-ham-so-yfleft-x-right-lien-tuc-tren-doan-left-12-right-va-thoa-fleft-x-rightsqrt2xx-fleft-3-x2-right-tinh-idisplaystyleint_-12fleft-x-righttextrm-d.html/feed 0 Xét hàm số $ y=f\left( x \right)$ liên tục trên đoạn $\left[ 0;2 \right]$ và thỏa $ f\left( x \right)+7f\left( 2-x \right)=2x$. Tính $I=\displaystyle\int_0^2{f\left( x \right)\textrm{ d}x}$. https://booktoan.com/xet-ham-so-yfleft-x-right-lien-tuc-tren-doan-left-02-right-va-thoa-fleft-x-right7fleft-2-x-right2x-tinh-idisplaystyleint_02fleft-x-righttextrm-dx.html https://booktoan.com/xet-ham-so-yfleft-x-right-lien-tuc-tren-doan-left-02-right-va-thoa-fleft-x-right7fleft-2-x-right2x-tinh-idisplaystyleint_02fleft-x-righttextrm-dx.html#respond Fri, 13 Mar 2020 00:08:22 +0000 https://booktoan.com/?p=172170 https://booktoan.com/xet-ham-so-yfleft-x-right-lien-tuc-tren-doan-left-02-right-va-thoa-fleft-x-right7fleft-2-x-right2x-tinh-idisplaystyleint_02fleft-x-righttextrm-dx.html/feed 0 Cho hàm số $ y=f\left( x \right)$ liên tục và có đạo hàm trên $\mathbb{R}$ và thỏa điều kiên $ f\left( x^3+3x+1 \right)=3x+2,\forall x\in \mathbb{R}.$ Tính tích phân $I=\displaystyle\int_1^5{x.f’\left( x \right)\textrm{ d}x}$ https://booktoan.com/cho-ham-so-yfleft-x-right-lien-tuc-va-co-dao-ham-tren-mathbbr-va-thoa-dieu-kien-fleft-x33x1-right3x2forall-xin-mathbbr-tinh-tich-phan-idisplaystyleint_15x-fleft.html https://booktoan.com/cho-ham-so-yfleft-x-right-lien-tuc-va-co-dao-ham-tren-mathbbr-va-thoa-dieu-kien-fleft-x33x1-right3x2forall-xin-mathbbr-tinh-tich-phan-idisplaystyleint_15x-fleft.html#respond Fri, 13 Mar 2020 00:01:31 +0000 https://booktoan.com/?p=172168 https://booktoan.com/cho-ham-so-yfleft-x-right-lien-tuc-va-co-dao-ham-tren-mathbbr-va-thoa-dieu-kien-fleft-x33x1-right3x2forall-xin-mathbbr-tinh-tich-phan-idisplaystyleint_15x-fleft.html/feed 0 Xét hàm số $ y=f\left( x \right)$ lên tục trên đoạn $\left[ 0;1 \right]$ và thỏa điều kiện $2f\left( x \right)+3f\left( 1-x \right)=x\sqrt{1-x}.$ Tính tích phân $I=\displaystyle\int_0^1{f\left( x \right)\textrm{ d}x}$ https://booktoan.com/xet-ham-so-yfleft-x-right-len-tuc-tren-doan-left-01-right-va-thoa-dieu-kien-2fleft-x-right3fleft-1-x-rightxsqrt1-x-tinh-tich-phan-idisplaystyleint_01fleft-x-rig.html https://booktoan.com/xet-ham-so-yfleft-x-right-len-tuc-tren-doan-left-01-right-va-thoa-dieu-kien-2fleft-x-right3fleft-1-x-rightxsqrt1-x-tinh-tich-phan-idisplaystyleint_01fleft-x-rig.html#respond Thu, 12 Mar 2020 23:43:29 +0000 https://booktoan.com/?p=172166 https://booktoan.com/xet-ham-so-yfleft-x-right-len-tuc-tren-doan-left-01-right-va-thoa-dieu-kien-2fleft-x-right3fleft-1-x-rightxsqrt1-x-tinh-tich-phan-idisplaystyleint_01fleft-x-rig.html/feed 0 Cho $ y=f\left( x \right)$ liên tục trên $\mathbb{R}$ và thỏa $ f\left( x \right)+2f\left( \dfrac{1}{x} \right)=3x$. Tính $I=\displaystyle\int_{\tfrac{1}{2}}^2{\dfrac{f\left( x \right)}{x}\textrm{ d}x}.$ https://booktoan.com/cho-yfleft-x-right-lien-tuc-tren-mathbbr-va-thoa-fleft-x-right2fleft-dfrac1x-right3x-tinh-idisplaystyleint_tfrac122dfracfleft-x-rightxtextrm-dx.html https://booktoan.com/cho-yfleft-x-right-lien-tuc-tren-mathbbr-va-thoa-fleft-x-right2fleft-dfrac1x-right3x-tinh-idisplaystyleint_tfrac122dfracfleft-x-rightxtextrm-dx.html#respond Thu, 12 Mar 2020 23:36:48 +0000 https://booktoan.com/?p=172164 https://booktoan.com/cho-yfleft-x-right-lien-tuc-tren-mathbbr-va-thoa-fleft-x-right2fleft-dfrac1x-right3x-tinh-idisplaystyleint_tfrac122dfracfleft-x-rightxtextrm-dx.html/feed 0 Cho hàm số $ y=f\left( x \right)$ có đạo hàm và liên tục trên đoạn $\left[ -1;1 \right]$, thỏa $ f\left( x \right)>0,\forall x\in \mathbb{R};$ và $ f’\left( x \right)+2f\left( x \right)=0$. Biết $ f\left( 1 \right)=1.$ Tính $ f\left( -1 \right).$ https://booktoan.com/cho-ham-so-yfleft-x-right-co-dao-ham-va-lien-tuc-tren-doan-left-11-right-thoa-fleft-x-right0forall-xin-mathbbr-va-fleft-x-right2fleft-x-right0-biet-fl.html https://booktoan.com/cho-ham-so-yfleft-x-right-co-dao-ham-va-lien-tuc-tren-doan-left-11-right-thoa-fleft-x-right0forall-xin-mathbbr-va-fleft-x-right2fleft-x-right0-biet-fl.html#respond Thu, 12 Mar 2020 23:27:33 +0000 https://booktoan.com/?p=172162 0,\forall x\in \mathbb{R};$ và $ f’\left( x \right)+2f\left( x \right)=0$. Biết $ f\left( 1 \right)=1.$ Tính $ f\left( -1 \right).$ A. $ f\left( -1 \right)={e^{-2}}.$ B. $ f\left( -1 \right)=e^2.$ C. […]]]> https://booktoan.com/cho-ham-so-yfleft-x-right-co-dao-ham-va-lien-tuc-tren-doan-left-11-right-thoa-fleft-x-right0forall-xin-mathbbr-va-fleft-x-right2fleft-x-right0-biet-fl.html/feed 0 Giả sử $ y=f\left( x \right)$ liên tục, nhận giá trị dương trên $\mathbb{R}$, thỏa $ f\left( 0 \right)=\dfrac{1}{2}$ và $ f’\left( x \right)+e^x.f^2\left( x \right)=0$, $\forall x\in \mathbb{R}.$. Tính giá trị $ f\left( \ln 2 \right)$ https://booktoan.com/gia-su-yfleft-x-right-lien-tuc-nhan-gia-tri-duong-tren-mathbbr-thoa-fleft-0-rightdfrac12-va-fleft-x-rightex-f2left-x-right0-forall-xin-mathbbr-tin.html https://booktoan.com/gia-su-yfleft-x-right-lien-tuc-nhan-gia-tri-duong-tren-mathbbr-thoa-fleft-0-rightdfrac12-va-fleft-x-rightex-f2left-x-right0-forall-xin-mathbbr-tin.html#respond Thu, 12 Mar 2020 23:20:25 +0000 https://booktoan.com/?p=172160 https://booktoan.com/gia-su-yfleft-x-right-lien-tuc-nhan-gia-tri-duong-tren-mathbbr-thoa-fleft-0-rightdfrac12-va-fleft-x-rightex-f2left-x-right0-forall-xin-mathbbr-tin.html/feed 0